Cellular/satellite communications system with improved frequency re-use

ABSTRACT

A satellite communications system employs a multiple element antenna for receiving signals on a first frequency band and relaying the signals to a ground station on a second frequency band. The system includes a downconvertor for converting signals received at each of the multiple antenna elements on the first frequency band to corresponding baseband signals, and a multiplexor for time-division multiplexing the corresponding baseband signals to form a multiplexed sample stream. The system also includes a modulator for modulating a carrier in the second frequency band with the multiplexed sample stream and transmitting the modulated carrier to the ground station. In exemplary embodiments, the downconvertor comprise a quadrature downconvertor producing an I and a Q baseband signal. The satellite relays signals received from the ground station using a demultiplexor in a similar manner.

This application is a divisional, of application Ser. No. 08/179.953,filed Jan. 11, 1994 now Pat. No. 5,619,503.

BACKGROUND

The present invention relates to radio communication systems withincreased capacity. The system can include a number of roving,automobile-mounted or handheld telephone sets served by either fixed,ground-based stations or by orbiting satellites or by a combination ofboth. The capacity of such systems to serve a large number ofsubscribers depends on how much of the radio spectrum is allocated forthe service and how efficiently it is used. Efficiency of spectralutilization is measured in units of simultaneous conversations (erlangs)per megahertz per square kilometer. In general, spectral efficiency canbe improved more by finding ways to re-use the available bandwidth manytimes over than by attempting to pack more conversations into the samebandwidth, since narrowing the bandwidth generally results in the needto increase spatial separation between conversations thus negating thegain in capacity. Therefore, it is generally better to increase thebandwidth used for each conversation so that closer frequency re-use ispossible.

Spread-spectrum communications systems (e.g., CDMA systems) thatincrease the signal bandwidths using heavy redundant coding, such that asignal can be read even through interference from other users, offerhigh spectral efficiency. Using such systems, several users in the samecell can coexist in the same bandwidth, overlapping in both frequencyand time. If co-frequency interferers in the same cell can be tolerated,co-frequency interferers one or more cells away can also be toleratedsince distance will lessen their interference contribution, so it wouldbe possible to re-use all frequencies in all cells.

Spread-spectrum system capacity is said to be self-interference limitedbecause each unwanted signal that is received simultaneously with thedesired signal, and on the same frequency, contributes an interferencecomponent. Some systems, however, such as satellite communicationssystems, are already limited by natural noise, so the widebandspread-spectrum approach is then not necessarily the best technique formaximizing capacity. Consequently it would be desirable to re-use thewhole spectrum in every adjacent cell or region without incurring theself-interference penalty of wideband spread-spectrum.

FIG. 1 shows a typical arrangement of a cellular telephone network usingland-based stations. This figure is illustrative of such networks only,for example, cells are not always of such regular size and shape and asa general definition a cell may be described as an area illuminated witha distinct signal.

Cells can be illuminated from their geographical centers, but it is morecommon to illuminate a cluster of three cells from a common site at thejunction of the three cells, as site real estate cost is a majoreconomic consideration. The antenna radiation patterns for centralillumination of a cell would generally be omnidirectional in azimuth. Itis also common to narrow the radiation pattern in the vertical plane soas to concentrate the energy towards land-based telephones and avoidwasting energy skywards. When the transmitters and antennas for threecells are collected onto the same site for economy, the antenna patternsare then only required to illuminate 120 degree sectors, and theresultant azimuthal directive gain largely compensates for the doubledistance to the far side of the cell. The antenna pattern can be shapedappropriately so as to provide a gain commensurate with the maximumrange needed in each direction, which is halved at +/-60 degreescompared to mid-sector. Thus a sectorized antenna pattern can benarrowed to -12 dB at +/-60 degrees, giving a mid-sector gain of about 8to 9 dB to assist in achieving the maximum range in that direction.

Using central illumination, the U.S AMPS cellular mobile telephonesystem denies re-use of the same frequency within a 21-cell area arounda given cell. This is called a 21-cell frequency re-use pattern andresults in co-channel interference being approximately 18 dB below awanted signal when all channels are concurrently in use (commonly calledmaximum load). Such a 21-cell re-use pattern is illustrated in FIG. 2.Certain re-use pattern sizes such as 3, 4, 7 and products thereof (e.g.,9, 12, 21 . . . ) result in co-channel interferers being equidistantfrom the wanted signal and located on the vertices of a hexagon,separated by a number of cells equal to the square root of the patternsize.

In practice, illumination takes place from sites at the junction ofthree cells. Although the re-use pattern is a 21-cell pattern, it canalso be described as 7-sites each having a 3-frequency re-use patternaround the three, 120 degree sectors. The signal to co-channelinterference characteristics arising from this form of illumination arenot exactly equivalent to those characteristics which result fromcentral illumination (due to the antenna directivity it can be shownthat interference with respect to a particular signal arises principallyfrom two other sites whose antennas are firing in the right direction,and not from six equidistant cells which transmit on a common frequencyas would be the case in central illumination).

The 3-sector, 7-site method of illumination is sometimes calledsectorization, which can give the erroneous impression that anoriginally larger cell was split into three smaller cells or sectors byuse of directional antennas. This impression, however, is inaccuratebecause the arrangement used for illuminating three cells from the samesite is merely an economic arrangement that actually has slightdisadvantages over central illumination with respect to technicalperformance but is otherwise very similar.

Cell-splitting is another concept entirely, being a way of obtainingmore capacity per square kilometer by providing base stations moredensely on the ground. Introducing cell splitting in an already existingsystem usually requires complete revamping of the frequency re-use plan,as it is conventionally not possible simply to split a cell, forexample, into three cells and to re-use the original frequencies threetimes over. This would result in the three new cells operating on thesame frequency with no spatial separation, which would present a problemfor a mobile phone on the boundary between two cells where it receivesequal strength (but different content) signals on the same frequencyfrom both. Thus, it would be desirable to allow a cell to be split intosectors with the same frequencies being used in each without theabove-described interference problem.

Similar capacity issues arise in designing a satellite communicationssystem to serve mobile or handheld phones. On handheld phones,omnidirectional antennas of indifferent performance are all that inpractice the majority of consumers are willing to accept. Directionalantennas that have to be oriented toward the satellite or larger, morecumbersome antennas do not now find favor in the marketplace, so it isnecessary for the satellite to provide a high enough signal strength atthe ground to communicate with such devices. The signal strengthreceived at the ground from a satellite is usually measured in units ofwatts per square meter or dBW per square meter on a logarithmic scale.For example, a flux density of the order on -123 dBW per square meter isused for voice communication to provide an adequate link margin formultipath fading, shadowing, polarization mismatch etc., using adownlink frequency of 2 GHz. The total number of watts radiated by thesatellite is then equal to this required flux density times the area ofthe geographical region it illuminates. For example, to provide such avoice channel anywhere in the entire United States, having an area of 9million square kilometers requires a total radiated power of:

10⁻¹².3 ×9×10¹² =4.5 watts from the satellite.

One voice channel would not, of course, provide a useful capacity. Fiveto ten thousand Erlangs is a more reasonable target for serving theUnited States. One way of increasing the capacity would be to generate4.5 watts on other frequencies too, each of which could carry one voicechannel; but a 45 k watt satellite would be very large and expensive tolaunch and would not be an economic way to provide 10000 erlangscapacity. It is therefore more efficient, having used 4.5 watts ofsatellite RF power to create one voice channel's worth of flux densityat all places in the United States, to find ways which will allow thevoice carried by that flux to be different at different places, thussupporting many different conversations using no more power orbandwidth.

The ability of a satellite to modulate the same radiated flux densitydifferently in different directions depends on the angulardiscrimination provided by its antenna aperture. The angulardiscrimination of an antenna (in radians) is on the order of the ratioof the wavelength to the diameter of the antenna. Using an exemplarydownlink frequency of 2 GHz (15 cm wavelength) an antenna of 1.5 metersin diameter theoretically has an angular discrimination on the order of1/10th of a radian or 5.7 degrees, which, from an orbital height of, forexample, 10000 kilometers, allows discrimination between 37 differentdirections within the United States coverage area. Thus, the same 4.5watts of satellite radiated power could then support not just one, but37 different conversations.

One way of creating 37 different beams is shown in FIG. 3. A parabolicreflector focuses the radio energy from a pattern of 37 different feedsdown to the earth. An image of the feeds is projected onto the groundforming the desired separately illuminated areas. Unfortunately, usingthis technique there is spillover from one area to another, and in anycase a mobile phone on the boundary between two or three cells receivesequal signals from two or three feeds. If these signals areindependently modulated, the phone receives a jumble of threeconversations which it cannot decipher. Accordingly, conventionalsystems have been unable to exploit the potential capacity increaseswhich would be realized using discrimination.

SUMMARY

These and other drawbacks and difficulties found in conventional radiocommunication systems, satellite communication systems and hybridsthereof are overcome according to the present invention.

According to exemplary embodiments of the present invention, matrixprocessing can be used to form numerical combinations of data samplestreams. The matrix coefficients are selected, and can be periodicallyadjusted, so that each of a plurality of receivers receives its intendedsignal with substantially zero interference.

According to another exemplary embodiment of the present invention,signal processing does not adapt to the movement of mobile phones or tonew call set-up and termination, but operates in a deterministic way andinstead the traffic is adapted to the deterministic characteristics ofthe signal processing using a dynamic traffic channel assignmentalgorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing, and other, objects, features and advantages of thepresent invention will be more readily understood upon reading thefollowing detailed description in conjunction with the drawings inwhich:

FIG. 1 illustrates a conventional land based cellular network;

FIG. 2 illustrates a conventional 21-cell frequency re-use plan;

FIG. 3 shows a conventional satellite implementation of 37 beamsilluminating a region of the Earth;

FIG. 4 illustrates an illumination pattern used to describe a feature ofthe present invention;

FIG. 5 shows a 3-cell frequency reuse plan;

FIG. 6 shows a satellite-mobile communication system according to anexemplary embodiment of the present invention;

FIG. 7 illustrates a mobile-to-hub transponder according to an exemplaryembodiment of the present invention;

FIG. 8(a) illustrates a hub-to-mobile satellite transponder according toan exemplary embodiment of the present invention;

FIG. 8(b) illustrates a combining network for a power amplifier matrixaccording to another exemplary embodiment of the present invention;

FIG. 9 shows a hubstation according to an exemplary FDMA embodiment ofpresent invention;

FIG. 10 illustrates coherent beam signal transmission according to anexemplary embodiment of the present invention;

FIG. 11 shows spectral characteristics using dual polarizations onk-bank hublinks according to an exemplary embodiment;

FIG. 12 is a block diagram illustrating phase coherent transportation ofthe beam signals according to an exemplary embodiment;

FIG. 13 is a block diagram illustrating phase coherent transportation ofbeam signals according to another exemplary embodiment of the presentinvention;

FIG. 14 illustrates mapping of 2-bit multiplexed I and Q signals to aK-band carrier vector;

FIG. 15 is a block diagram illustrating yet another exemplary embodimentof phase coherent beam signal transportation;

FIG. 16 is a block diagram illustrating hubstation transmit signalprocessing according to an exemplary TDMA embodiment of the presentinvention;

FIG. 17 illustrates connections between a receive control processor anda transmit control processor according to an exemplary embodiment of thepresent invention;

FIG. 18 shows, a land-cellular exemplary embodiment of the presentinvention;

FIG. 19 is a block diagram illustrating the maximum likelihooddemodulation of signals from an antenna array according to an exemplaryembodiment of the present invention;

FIG. 20 shows an exemplary arrangement of staggered sector patterns;

FIGS. 21(a) and 21(b) illustrate progressive illumination patternsaccording to an exemplary embodiment of the present invention;

FIG. 22 is a block diagram illustrating part of an exemplaryimplementation of a dynamic channel assignment embodiment of the presentinvention;

FIG. 23 graphical representation of an exemplary radiation pattern for acircular-symmetric, uniform aperture illumination function;

FIG. 24 is an exemplary graph of relative signal gain versus beamcrossover points;

FIG. 25 is an exemplary graph illustrating C/I versus mobile position incell for 3-cell frequency re-use pattern;

FIG. 26 is an exemplary graph illustrating C/I versus beam edgecrossover point;

FIG. 27 is an exemplary graph illustrating C/I versus mobile position incell for an immediate frequency re-use system;

FIG. 28 an exemplary graph illustrating C/I versus beam edge crossoverpoint for an immediate frequency re-use system;

FIG. 29 illustrates an exemplary radiation pattern for acircular-symmetric, 1/2 cosine aperture illumination function;

FIG. 30 is an exemplary graph of relative signal gain versus beamcrossover points for the illumination function pattern of FIG. 29;

FIG. 31 is an exemplary graph illustrating C/I versus mobile position incell for a 3-cell re-use pattern for the illumination function of FIG.29;

FIG. 32 is an exemplary graph illustrating C/I versus beam crossoverpoint at all mobile positions within 25% of cell radius for a 3-cellre-use pattern fore illumination function of FIG. 29;

FIG. 33 is an exemplary graph illustrating C/I versus mobile position incell for immediate frequency re-use for the illumination function ofFIG. 29;

FIG. 34 is an exemplary graph illustrating C/I at all points within 25%of beam radius as a function of dB down at beam edge crossover for animmediate frequency re-use system using the aperture illuminationfunction of FIG. 29;

FIG. 35 Illustrates beam and cell patterns according to an exemplaryembodiment of the present invention;

FIG. 36 Illustrates another exemplary beam and cell pattern using sevencommunication channels;

FIG. 37 is a block diagram of a fixed beam forming apparatus accordingto yet ether exemplary embodiment of the present invention;

FIG. 38 is a diagram of current injection and extraction pointsillustrating a beam forming apparatus according to an exemplaryembodiment of the present invention; and

FIG. 39 illustrates an exemplary TDMA embodiment of the beam formingapparatus of FIG. 37.

DETAILED DESCRIPTION

Initially, it is helpful to understand the interference problemsassociated with the transmission of signals from conventional antennaarrays, such as the one illustrated in FIG. 3. FIG. 4 illustrates across section of the illumination intensity produced on the ground froman antenna, such as the antenna shown in FIG. 3. Even for a bestinterference case where a mobile unit is located at the center of beam 2(point A) the illumination from beams 1 and 3 is not zero, but onlysomewhat reduced. The total signal received by mobile 2 can be describedas the sum of three components, such as:

an amount C21 times the beam 1 signal S1 (small)

an amount C22 times the beam 2 signal S2 (large)

an amount C23 times the beam 3 signal S3 (small)

Considering now the reverse (uplink) direction, and assuming reciprocalpropagation, the satellite receives in beam 2 a contribution from threemobiles, namely C21.M1+C22.M2+C23.M3 where M1, M2, M3 are respectivelythe signals radiated from mobiles in cells 1, 2 and 3. If mobile 1 isnot close to the edge of beam 2, C21 will be small; since mobile 2 iswithin beam 2, C22 will be large; and if mobile 3 is not close to theedge of beam 2, C23 will be small. Thus as long as mobiles are ideallyplaced and not on the edges of cells, it may be that the level ofinter-cell interference can be tolerated.

On the other hand, if a mobile unit is, for example, close to theboundary between cell 1 and cell 2, the coefficient C21 will be largeand M1 will interfere with the decoding of signal M2. The conventionaltechnique for avoiding this problem is to deny use of the same frequencyin immediately adjacent cells. For example, the 3-cell frequency re-usepattern shown in FIG. 5 might be used. The shaded cells in FIG. 5 arethose using a first frequency f1, while the other cells use f2 and f3 inthe indicated pattern. It can be seen that cells using the samefrequency f1 do not abut, and have edge-to-edge separations of just lessthan one cell diameter. A mobile on the edge of one beam is quite fardown the illumination intensity curve of other cells using the samefrequency, and thus avoids interference. However, the drawback is thatonly one-third of the available frequencies may be used in each cell,reducing the spectral utilization efficiency by a factor of three.Accordingly, the present invention provides, among other features, ameans of cancelling the co-channel interference without the loss ofspectral efficiency entailed in denying spectral re-use in adjacentcells.

If the expressions for the signals received in all beams B1, B2, B3 . .. etc., are collected together, and we assume for the moment the samenumber of mobile signals as beams, then the following set of equationsresults: ##EQU1## which can be abbreviated to B=C.M where B and M arecolumn vectors and C is a square, n×n matrix of coefficients.

From the signals received by the satellite in each of its beams, it isdesirable to determine the signals transmitted by the mobiles; accordingto the present invention this can be done by solving the above set ofequations to obtain:

    M=C.sup.-1.B

This solution can be obtained as long as the matrix C is invertible(i.e., has a non-zero determinant) and results in cancellation ofsubstantially all interference between mobile signals and completeseparation therebetween. All the elements of the above equations, thatis mobile signals Mi, beam signals Bk and matrix elements Cki, arecomplex numbers having both a real and an imaginary component so as tobe able to represent not only signal amplitude differences but alsosignal phase relationships. According to the present invention thesignals received in the different antenna beams are sampled at the sametime at a rate sufficient to capture all signal components of interestaccording to Nyquist's criteria. One set of such samples forms thecolumn vector B at any instant, and each such vector is multiplied bythe inverse of C, for example, once per sample period to obtain a set ofsamples M representing interference free mobile signals. Successivevalues of the same element of M form the sample stream corresponding toone mobile signal. This stream is fed to a digital signal processor foreach mobile signal that turns the sample stream into, for example, ananalog voice waveform or 64 KB PCM digital voice stream as required bythe telephone switching system to which the system is connected.

According to another aspect of the present invention, the matrix C doesnot have to be inverted every sample period, but can be inverted lessfrequently or only once at the beginning of a call. The matrix C and itsinverse vary relatively slowly because the rate at which the Ccoefficients change due to the mobile unit shifting position within thebeams, or due to the beam illumination intensity distributions changingdue to satellite movement in the non-geostationary case, is relativelylow. In an exemplary satellite embodiment of the present invention,typical cell sizes are in the hundreds of kilometers diameter range andsatellites orbiting at medium altitudes take an hour or two to pass by atypical cell. Thus the need to compute a new matrix inverse due tomovements may not arise for the duration of, for example, a typical3-minute telephone call. The principal reason that changes in theinverse C-matrix would be beneficial, however, is that conversations arecontinually being connected and disconnected. If n=37, for example, andthe average call duration is 3 minutes, then on the average one mobileand its corresponding column of matrix C drops out and is replaced withanother column of coefficients every 5 seconds. The process whereby newinverse C matrices are introduced when this occurs will be explainedlater, suffice it to say that this represents a relatively negligiblecomputational effort compared to the total digital signal processinginvolved in demodulating and decoding 37 mobile signals.

An exemplary embodiment which applies these principles will now bedescribed with reference to FIGS. 6-11.

FIG. 6 illustrates a plurality of portable stations 420 in communicationvia satellite 410 with a hubstation 400. The hubstation is connected,for example via a local exchange, to a public switched telephone network(PSTN) to allow calls to be placed between the portable phones and anytelephone subscriber worldwide, as well as between the satellite phones.The satellite receives signals from the portable phones at a relativelylow microwave frequency, such as 1600 MHz. At such frequencies thetransmitters in battery operated phones can be efficient and theirantennas can be small and omnidirectional. The satellite translates thereceived signals from 1600 MHz to a higher frequency for relaying to thehubstation.

A higher frequency can be used because the bandwidth needed on thesatellite-to-hub link is at least n times the bandwidth allocated at1600 MHz for each beam, where n is the number of beams. For example, if6 MHz of bandwidth is re-used in each of 37 beams at 1600 MHz, then atleast 37×6 or 222 MHz of bandwidth will be needed on the satellite-hublink. Since one method of maintaining coherent beam signal transportuses at least twice this bare minimum bandwidth, and the reversedirection requires the same amount, 1 GHz of bandwidth is needed. Thissuggests that a carrier frequency around, for example, 20 GHz isappropriate for the satellite-hub forward and return links.

At such a frequency, even relatively small hubstation dishes will havevery narrow beamwidths, so that exclusive use of this bandwidth by anyone system is not necessary, and the entire bandwidth can bere-allocated to other satellites and ground stations withoutinterference as long as the sightilne from a first ground station to afirst satellite does not intersect with a second satellite. This can beavoided by allocating unique "stations" to satellites in geostationaryorbit, or, in the case of lower orbiting satellites that move, theprobability of intersection is low and can be handled by having analternative hub location which is activated when such an eventthreatens.

FIG. 7 shows a block diagram of an exemplary satellite transponder forrelaying mobile-originated signals to the hubstation. The L-band (e.g.,1600 MHz) multi-beam satellite antenna 470 receives signals from aplurality of mobile phones distributed between the various beams andamplifies them in respective low-noise amplifiers 480. The compositesignal from each beam contains, for example, signals from 400-500 mobilephones using different frequencies spaced at 12.5 KHz intervals over atotal bandwidth of 6 MHz. The composite signals of each beam aredownconverted in respective mixers 440 to obtain baseband signals, forexample, spanning the range of 1-7 MHz. This type of signal will bereferred to hereafter as a "video" signal as it is typical of thefrequency range spanned by signals from a TV camera. To downconvert thecomposite received signal to the video signal, the downconverters can,for example, be image-rejection type downconverters. The downconversionprocess can optionally take place in one or more steps using appropriateintermediate frequencies.

The downconvertors in the system can use the same local oscillatorsignal so as to preserve the phase relationships at the downconvertedfrequencies that were received at the antennas. The inadvertentintroduction of fixed phase mismatches and small amplitude differencesbetween channels is not a problem as this can be calibrated out byanalog or digital processing at the hubstation.

The baseband signals are used to modulate respective carriers at thesatellite-hub frequency band, e.g., 20 GHz. If single-sidebandmodulation of a 1-7 MHz "video" signal were applied to a 20 GHz carrierfrequency, the resulting signal would occupy the frequency range 20.001to 20.007 GHz. However, using single-sideband modulation can make itdifficult to preserve the phase coherency between the beam signals.Accordingly, double-sideband modulation techniques can be used instead.For example, the 1-7 MHz video signal can be used to frequency or phasemodulate a 20 Ghz carrier frequency. The frequency range occupied by themodulated carrier would then be approximately 19.993-20.007 MHz, ormore, depending on the frequency or phase deviation employed. To allowsome margin over the bare 14 Mhz bandwidth, a 25 Mhz carrier spacingmight be appropriate in the 20 Ghz band. Thus, 37×25 or 925 MHz can beused for the one-way satellite-hub link. This bandwidth can be halved byintelligent use of orthogonal polarizations as described later.

FIG. 8(a) shows an exemplary satellite transponder for the hub-mobilerelay direction. The same method described above for the mobile-to-hubtransmissions can be used in reverse for the coherent transport ofmultiple beam signals to the satellite. The hub station (not shown)transmits a number of Ka band frequency or phase modulated carriers tothe satellite. These are received using a suitable Ka band antenna 360,amplified in a common low-noise amplifier 350, and then fed to FMreceiver bank 340 where each carrier is demodulated by a respectivereceiver to produce a video frequency version of the signals fortransmission in respective beams. These video signals, for exampleoccupying the band 1-7 MHz, are then upconverted in respectiveupconverters 320, using a common local oscillator 330 to preserverelative phase relationships, and then amplified using power amplifiermatrix 310 for transmission via multi-beam antenna 300 to the mobilephones. A suitable frequency for the satellite-to-mobile link is, forexample, 2.5 GHz (S-band). The amplifiers in the power amplifier matrixcan be linear amplifiers to reduce intermodulation between signalsdestined for different phones. The power amplifier matrix can forexample, either be a bank of n separate amplifiers each associated withrespective beams, or a bank of N (greater or equal to n) amplifierscoupled by n×N Butler matrices at their inputs and N×n Butler matricesat their outputs. The effect of the Butler matrices is to use eachamplifier to amplify part of every beam signal, thus evening the load,providing graceful degradation in the event of failure, and reducingintermodulation by absorbing a proportion of the intermodulation energyin N-n dummy loads. Examples of such power amplifier matrixes can befound in U.S. Pat. No. 5,574,967, entitled "Waste Energy Control andManagement in Power Amplifiers" and filed on Jan. 11, 1994 which isincorporated here by reference.

According to another exemplary embodiment of the present invention, incommunication systems using TDMA signals relayed through anearth-orbiting satellite having a communications transponder using sucha matrix power amplifier, the power amplifier can have its input Butlercombining network located at the ground station instead of thesatellite. A Butler combining operation may be performed by digitalsignal processing at the ground station to form weighted sums of thedesired beam signals to generate drive signals corresponding to eachamplifier of the matrix power amplifier. These weighted sums aretransmitted using coherent feeder links to the satellite'scommunications transponder which receives them and translates them to asecond frequency band for driving the power amplifier in such a waythat, after Butler combining the power amplifier outputs, the outputsignals correspond to signals desired to be transmitted in differentantenna beam directions to respective ground-terminals, which may be,for example, a small handportable station.

The resulting satellite circuitry is shown in FIG. 8(b). Note that theinput combiner which is normally present has been omitted since thisfunction is now performed at the ground station, as illustrated by thedashed rectangular outline 800. The antenna 810, signal processingincluding linear amplifier 820, feeder link receivers and downconverters830 and output combiner 840 can be implemented in the conventionalmanner and thus are not further described herein.

This embodiment may be advantageous for certain situations, for example,dynamic reallocation of power between antenna beams and timeslots may beaccomplished without large variations in the corresponding forwardfeeder link signals, because each feeder link carries part of everybeamsignal instead of all of one beam signal. Additionally,pre-distortion of signals sent on the forward feeder links may beapplied to further compensate for distortion in the associatedtransponder channel power amplifiers. Moreover, in the case of theover-dimensioned matrix power amplifier described in theabove-incorporated "Waste Energy Control and Management in PowerAmplifiers" application, the number of feeder links is greater than thenumber of independent beam signals to be created, thus affording ameasure of redundancy against failure.

FIG. 9 shows a block diagram of a hubstation according to an exemplaryembodiment of the invention. The hub antenna 600 receives Ka bandcarriers from the satellite and, after common low-noise amplificationand optional downconversion in block 610, the signal is divided betweena number of receivers for respective Ka-band carriers to obtain the beamsignals B_(l) . . . B_(n). Each beam signal is composed of amultiplicity of voice-modulated channel frequencies which are separatedin channel separation filters 630.

The channel separation filters 630 can be analog components such ascrystal filters, and may involve frequency conversion of a selectedchannel frequency to a common lower frequency (e.g., 12.5-25 KHz, or 455KHz) for A/D conversion. The selected channel signal having beenconverted to a suitable frequency is A/D converted in A/D convertors640. An exemplary A/D convertor technique suitable for use at lowintermediate frequencies such as 455 KHz is the technique described inU.S. Pat. No. 5,048,059 to Paul W. Dent entitled "Log-Polar SignalProcessing", which is incorporated here by reference, which preservesthe full complex nature of the signal by simultaneously digitizing itsphase and its amplitude. Instantaneous phase can be digitized forexample, using the technique described in U.S. Pat. No. 5,084,669 toPaul W. Dent entitled "Direct Phase Frequency Digitization", which isalso incorporated here by reference. Phase digitization of all n beamsignals corresponding to one channel frequency can be carried out usingthe technique described therein by repeating certain elements (i.e., thetrigger circuits and holding registers) n times and sharing others(i.e., the reference frequency counter) as necessary to preserverelative phase coherency. Alternately, digital filters can be usedinstead of analog filters if the composite beam signals are firstdigitized, in which case the A/D converters 640 in FIG. 9 would not beneeded.

The numerical results of A/D conversion are fed sample by sample tonumerical matrix processor 650. There is one such processor per channelfrequency, but only the processor for channel frequency (m) is shown forclarity. The matrix processor processes the digitized beam signals toseparate out up to n separate mobile phone transmissions M_(l) . . .M_(n) and transfer a sample stream corresponding to each mobile phonetransmission to voice channel processor 660. The voice channel processornumerically performs demodulation of the signal and error correctiondecoding and transcoding of digitized voice from the bit rate and formatused over the satellite to standard PCM telephone system format forconnection via a digital exchange (not shown) to the PSTN. Thus theexemplary structure shown in FIG. 9 accomplishes decoding of nxm voicechannels, where n is the number of beams and m is the number offrequencies per beam. For example, with n=37 and m=400, the system has a14800 voice channel capacity potential.

The explanation of FIG. 9 relates to a system wherein one voice channelis carried per frequency (i.e., a Frequency Division Multiple Access(FDMA) system). However, the present invention can also be applied toTime Division Multiple Access (TDMA) systems. In TDMA systems, severalmobile phone signals are carried on the same channel frequency bydividing a repetitive frame period into time slots, and allocating onetime slot in each frame to one mobile phone signal. The exemplary blockdiagram of FIG. 9 can be applied even when the sample streams from A/Dconvertors 640 represent TDMA signals. However, the matrix processor 650will now separate a different set of mobile signals in each timeslot, sothat the matrix coefficients are now multiplexed between several sets,each of which correspond to a time slot. This can be an economicarrangement because, for a given number of voice channels complexity,the channel filters 630 will be fewer in number by a factor equal to thenumber of timeslots per carrier, the A/D convertors are correspondinglyfewer, the number of matrix processors is reduced correspondinglyalthough each has to operate at a higher input sample rate, and eachvoice channel processor can sequentially process the signals inconsecutive timeslots and thus achieve the same total number of voicechannels capacity while economically time-sharing components.

Each numerical matrix processor 650 is shown receiving a control signal.This control signal can be generated by a separate computer (not shown)which controls the connecting and disconnecting of calls to mobilephones, requiring changes to the matrix of coefficients used by theprocessor for separating out mobile signals from the beams. It wasmentioned earlier that this separation can be achieved if the inverse ofthe C matrix was not numerically ill-conditioned. If two mobiles arelocated exactly at the same point on the earth, their two correspondingcolumns of the C matrix will be identical, which causes the determinantto be zero and the inverse not to exist. Thus, for the C-matrix to beinvertible the mobiles shall be spaced far enough apart on the ground.If they approach each other too closely, the C-matrix becomesill-conditioned.

According to an aspect of the present invention, however, when thissituation threatens, one of the two (or more) approaching mobileschanges frequency to a channel where the other mobiles using the samefrequency are adequately separated. It is the function of the controlcomputer to determine, at least at call set-up and optionally atintervals thereafter, which of the available channel frequencies is mostsuitable for allocating to a new mobile, or for handing over an ongoingconversation. If there is no free capacity in a system the system issaid to be blocked and subscribers cannot place calls, much to theirannoyance. When the system is underloaded there are, at least on somefrequencies, fewer mobile signals than beams, thus the matrix C is notsquare. It will be shown later how the excess degrees of freedomprovided in underloaded systems can then be used, not only to separatemobile signals from each other thus avoiding mutual interference, butalso to maximize the signal quality received from the worst-case mobile.This solution changes when an extra mobile signal has to be accommodatedand the control computer can evaluate in advance the potential impact onsignal qualities. Thus a strategy for allocating a channel according toan exemplary embodiment of the present invention is to evaluate theimpact on the signal quality corresponding to the worst case mobile oneach channel through the inclusion of the new signal in thecomputations. The channel which suffers the least degradation, or meetsthe highest quality for the worst-case mobile, is then logicallyselected as the one to use for the new signal. This results in the groupof mobiles assigned to the same frequency being as widely spatiallyseparated as possible.

FIG. 10 shows an exemplary arrangement for coherent transmission of"video" signals from each beam. The video signal from the first antennafeed element's (beam) downconvertor (not shown) is fed to the voltagecontrol input of a 20 GHz voltage controlled oscillator (VCO) 1000. Thevideo signal frequency modulates the VCO. Successive VCO's with theircenter frequencies offset by the desired channel spacing (e.g., 25 MHz)are used for the signals from antenna feed elements 2,3 . . . to n/2.The VCO center frequency for signal 2 according to this exemplaryembodiment is 25 MHz (i.e., 1 GHz/40) higher than that for signal 1, andthe VCO 1001 frequency for signal n/2 is thus (n/2-1)×1 GHz/40=(n-2)/80GHz higher than that for signal 1. The signals from the VCOs are summedin summer 1002 which can be, for example, a waveguide or striplinedirectional coupler network, and the sum is amplified in a commonamplifier 1003 which can, for example, be a travelling wave tubeamplifier (TWTA).

A parallel arrangement is used to deal with the other half of the videosignals numbered n/2+1 to n. The VCO 1004 for signal n/2+1 is offset byhalf a channel spacing (i.e., by 12.5 MHz in the above example wherechannel spacing is 25 MHz) from that of VCO 1000 and this offset ismaintained up to VCO 1005 such that the set of frequencies used in theparallel arrangement are all offset half of a channel from those of thefirst arrangement. This minimizes any interference which may be causedby imperfect polarization isolation in the dual polarizationtransmission system. The outputs of the two TWTAs are connected to, forexample, dual-circular-polarized horn antenna 1009 via a polarizer 1008.The function of the polarizer 1008 is to launch a Right Hand circularlypolarized signal into horn antenna 1009 corresponding to the signal fromTWTA 1003 and simultaneously a Left Hand Circularly polarized signalcorresponding to the signal from TWTA 1007.

At the hubstation, the composite signal is received by a dual circularlypolarized antenna and the two polarizations are split into tworespective banks of FM receivers. The center frequencies of the FMreceivers correspond to the center frequencies of the VCOs of FIG. 10.The demodulated outputs from the FM receivers reproduce the signalsreceived at the satellite L-band antenna elements preserving their phaseand amplitude relationships. FIG. 11 shows an exemplary relationshipbetween the K-band transmission spectra for the two polarizations,showing how the half-channel offset between the RHC and LHC centerfrequencies minimizes interaction.

Those skilled in the art will readily appreciate that the block diagramsof FIG. 10 is merely illustrative of an exemplary arrangement ofcoherent signal transmission according to the present invention and thatmany functional equivalents flow therefrom. For example, it might beadvantageous first to generate the frequency modulated signals at alower frequency than 20 GHz, for example 2-3 GHz and, after summing, toconvert the composite signal to 20 GHz by mixing the summed signal witha common 18 GHz local oscillator and selecting the upper sideband with abandpass filter.

The above discussion has centered on the coherent transportation ofsignals received by the satellite L-band antenna elements to thehubstation. The same function, namely the transportation of signalsgenerated at the hubstation, is used in reverse for radiation byrespective satellite antenna elements, e.g., by the transponder of FIG.8. The hubstation can use a similar arrangement to FIG. 10, but with aset of K-band frequencies different from those used in thesatellite-to-hub direction, and with a larger antenna at the ground end.The satellite can employ a second, dual-polarized horn antenna forreception, or alternately use the same horn antenna and polarizer 1008and 1009 as in FIG. 10 with the addition of a transmit/receive diplexingfilter for each polarization to separate the transmit and receivesignals. Linear amplifier 350 can be duplicated for each polarizationand used to feed respective halves of FM receiver bank 340. The samehalf-channel frequency offset between the carriers of the twopolarizations is also advantageous in the hub-to-satellite direction.

FIG. 12 shows an alternative arrangement according to another exemplaryembodiment of the present invention for coherently transporting multiplesignals between the hub and the satellite. In this figure, eachsatellite transponder channel corresponding to one antenna feed elementis shown as a double downconversion process comprising an antenna filter1200, a low-noise amplifier 1201, image rejection filter 1202, firstdownconvertor 1203, IF filters 1204, 1206, IF amplifier 1205 andquadrature downconvertors 1207, 1208. The first downconvertors 1203 canuse the same local oscillator signal for all channels to preserverelative coherency. The quadrature downconvertors 1207 and 1208 can usethe same second local oscillator cosine and sine reference signals forall channels, again to preserve relative coherency. The quadraturedownconvertor outputs, for example in the 0-3 MHz range, are split incross-over network 1209 into 0-50 KHz components on lines 1215 and 1216and 50 KHz-3 MHz components on lines 1217 and 1218. The 50 KHz to 3 MHzcomponents correspond to uplink traffic channels using, for example,FDMA, an FDMA-plus-narrowband-CDMA hybrid or narrowband FDMA/TDMA, andare used to modulate separate I and Q K-band transmitters for relayingthese signals coherently to the hubstation. These components modulatethe I and Q voltage controlled oscillators 1210 and 1211. The outputs ofthese oscillators are summed in a K-band summing network and the sum fedto a common TWTA for amplification to the desired downlink transmitpower level. It is also advantageous to combine half the VCOS, e.g., theI VCOs into a first TWTA to form a signal for transmitting using RHCpolarization, the other half being transmitted with LHC. A similararrangement can be employed at the hubstation for coherently conveyingthe composite signal for each beam to the satellite.

The corresponding K-band receivers would comprise an FM receiver foreach of the I signals and an FM receiver for each of the Q signals.These FM receivers would preferably have automatic frequency control(AFC) which removes DC and low frequency components of the I and Qsignals, equivalent to having a notch in the frequency response in thecenter of the channel. This is of little consequence for wideband TDMAsignals and for FDMA simply means not using the channel in the center ofthe band for traffic.

In the satellite, the outputs of the K-band receivers are reconstitutedI and Q signals that are used to modulate COS and SIN L-band carriersusing a quadrature modulator to produce coherent beam signals. These areapplied to L-band power amplifiers for each beam or to the PA of theaforementioned matrix type.

The frequency arrangements used can be similar to those depicted in FIG.11, with RHC polarization being used, for example, for I components andLHC polarization for Q components, and the carrier spacings beingreduced such that they are commensurate with a 3 MHz modulating signalinstead of 7 MHz. A half-channel offset between the RHC- andLHC-polarized carriers is also advantageous in this I,Q method.

The I and Q signals represent, respectively, the projections of thecomplex received signal vectors on the real and imaginary axes, andpreserving the correct amplitude relationships between the I and Qsignals will then preserve the vector relationships including relativephase. The 2 n I and Q video signals can be used to frequency modulate 2n K-band carriers having less than half the channel spacing previouslyused in FIG. 10, for example 10 MHz. While it may appear more spectrallyefficient at K-band to use this method, it is difficult in practice tohandle I,Q signal components down to true zero frequency due to DCoffsets and frequency errors.

Consequently it is desirable to employ AC coupling and thus exclude aportion, for example 0-50 KHz, of the 0-3 MHz video signals fromtransmission. This places a notch in the center of the 6 MHz wide L-bandbandwidth that is transponded by this exemplary method. Depending on thenature of the signals, this notch may be of no consequence. For example,in copending, commonly assigned U.S. Pat. No. 5,539,730, entitled"TDMA/FDMA/CDMA Hybrid Radio Access Methods" granted Jul. 23, 1996,which is incorporated here by reference, there is disclosed a hybridaccess method suitable for satellite-cellular applications in whichsignals are conveyed on the downlink (satellite-mobile) by wideband TDMAin which each mobile signal occupies an assigned timeslot in arepetitive frame structure, and on the uplink (mobile-to-satellite) byFrequency Division Multiple Access (FDMA) or a combination of FDMA andCode Division multiple Access (CDMA). For example, a 6.5536 megabit persecond TDMA signal comprising 512 timeslots can be transmitted from thehubstation for transponding through the 6 MHz bandwidth of eachsatellite antenna feed element to a corresponding number of mobilephones in each cell. The omission of a small fraction of the bandwidthin the center of the channel will not disturb the character of such asignal significantly, and such disturbance as may occur can becompensated at the receiving radio using the technique for DC offsetcompensation disclosed in commonly assigned U.S. Pat. No. 5,241,702 toPaul W. Dent entitled "D.C. Offset Compensation in a Radio Receiver"which is incorporated here by reference.

When such 512-timeslot TDMA formats are used on the downlink, one ormore timeslots can be dedicated for use as a common signalling channel,also known as a calling channel, forward control channel, or pagingchannel. The calling channel is used by the system to broadcast calls tomobile phones originating from the network (e.g., from a PSTN subscriberor from another mobile phone). When a mobile detects its own phonenumber or ID in such a broadcast message, it replies using acorresponding uplink channel commonly called the "random accesschannel". The random access channel is so called because it is also usedby mobile phones to place mobile-originated calls, that is to requestservice from the network. With a large population of roaming mobilephones, these requesting events seem to the system to arise more or lessat random.

According to the aforementioned "TDMA/FDMA/CDMA Hybrid Access Methods"patent application, there is associated with each downlink timeslot acorresponding uplink carrier frequency. Thus to employ theaforementioned disclosure in conjunction with the I, Q version of thepresent invention, the uplink carrier frequency associated with thedownlink calling channel timeslots can be chosen to correspond to the+/-50 KHz in the center of the 6 MHz bandwidth and is used as the randomaccess channel.

Accordingly, the 0-50 KHz signals from the crossover network 1209represent random access signals and because of their relatively lowbandwidth the option of digitizing on-board and transmission by digitalmeans to the hubstation exists. This is carried out by A/D convertors1212, the outputs from each channel of which are multiplexed inmultiplexer 1213 to form a composite bitstream on the order of 60 MB/swhich modulates a digital transmitter 1214 for transmission to thehubstation.

According to yet another exemplary embodiment, antenna element signalscan be transported coherently between the ground station and thesatellite without bandwidth expansion. FIGS. 13 and 14 illustrate anexemplary coherent transmission method and apparatus which is based onanalog to digital conversion of each of the antenna signals followed bydigital multiplexing and then modulation of the multiplexed stream on tothe K-band feeder link carrier by means of Quadrature Amplitudemodulation. FIG. 15 illustrates an alternative apparatus derived fromFIG. 13 which equates to infinite AtoD and DtoA precision, thuspermitting the AtoD's and DtoA's of the exemplary embodiment of FIG. 13to be replaced by analog multiplexing.

With reference to FIG. 13, operation of this coherent transmissionsystem is as follows. A 2 GHz signal received from one of a plurality ofsatellite-borne antenna elements is low-noise amplified anddownconverted against cosine and sine local oscillator signals usingmixers 1301 and 1302. If the bandwidth at 2 GHz that is downconverted is5 MHz, then the resulting I and Q signals are of bandwidth 2.5 MHz each.Thus the desired bandwidth of 5 MHz may be imposed by the use of 2.5 MHzcut-off low pass filters 1304, 1305 operating on the I and Q signals.These mixers, filters and AtoD convertors 1306, 1307 are repeated foreach separate antenna element signal so treated. The mixers can receivethe same local oscillator signals cos(wT) and sin(wT) so as not tointroduce any relative phase shift between channels.

The baseband I and Q signals after filtering are converted using AtoDconvertors 1306 and 1307. These are arranged to sample and convert the Iand Q signals at least at the Nyquist rate, which is twice the bandwidthor, in this example, 5 MS/S. Sampling at least at the Nyquist rateallows the signals to be faithfully reconstructed from the samples. Byway of example, the AtoD convertors are illustrated as having only twobits resolution, that is each I or Q signals is classified as lyingnearest to one of the four values -3, -1, +1 or +3 arbitrary units, asindicated by a digital code 11, 10, 01 or 00.

In certain applications, two bits quantizing may indeed be sufficient.Such applications are characterized by the total signal-to-noise ratioin the 5 MHz bandwidth at 2 GHz being very low or even negative. Thiscan arise, for example, when the signal bandwidth has artificially beenwidened by the use of coding or spread-spectrum techniques. If thesignal-to-noise ratio is low or negative, a few bits resolution sufficeto make the digital quantizing noise lower than the radio noise to avoiddegradation. Those skilled in the art will appreciate that forapplications having higher signal-to-noise ratios, more bits can be usedto provide greater precision.

With the two-bit example, bit-pairs representing instantaneous I samplesand Q samples are collected from all antenna elements and multiplexedusing digital multiplexers 1308 and 1309. The output of digitalmultiplexers 1308 and 1309 is a two-bit I and two-bit Q signal,respectively, for antenna number 1, followed by the same for antennanumber 2, then 3, 4, etc., until antenna 1 is again sampled. Thesuccession of two-bit values of I and Q is then to be transmitted bymodulation onto the K-band feeder link carrier frequency.

Since the number of bits per second is 4N×5 MS/S=20N Mbits/S, abandwidth-efficient digital modulation scheme is required to avoid thesignal occupying more than the 5N MHz of the original N signals. Asuitable modulation scheme can, for example, be 16 QAM. In 16 QAM, fourbits of data are conveyed per transmitted symbol, by mapping two bits toone of four K-band carrier real vector values (i.e., the amplitude of acosine carrier component) and two bits to one of four imaginary vectorvalues (i.e., the amplitude of the sine component). The 4×4 grid ofpossible points that result is shown in FIG. 14. Using 16 QAM, Ibitpairs are mapped to the K-band I axis and Q bitpairs to the K-band Qaxis using DtoA convertors 1310 and 1311. Finally, the desired K-bandvector components are formed by applying the outputs of two-bit DtoAconvertors 1310 and 1311 to a K-band Quadrature Modulator 1312 which isdriven by K-band cosine and sine carrier waves (not shown) to form amodulated output signal for transmission via the K-band feeder linkantenna (also not shown).

The multiplexer can preferably have more inputs than signals fromantenna channels. For example, a typical antenna arrangement can be ahexagonal array of 61 antenna elements. A 64-input multiplexer can thenbe suitable, as a power of two arises naturally in multiplexerconstruction. The 3 spare inputs can then be connected to reference I,Qsignals equal respectively to (0,0), (1,0) and (0,1). The ground stationreceiver can use these reference signals to synchronize itsdemultiplexing and to determine quadrature modulator carrier leakage(offset) from the (0,0) case, and to provide phase references from the(1,0) and (0,1) cases for discriminating the I-axis bits from the Q-axisbits.

In case two-bit quantization is inadequate, AtoD convertors 1306 and1308 can be of a higher resolution, for example four bits. Then each4-bit I and 4-bit Q sample will represent one of 256 possibilities, andthis can be transmitted using 256 QAM in the same way as described abovefor 16 QAM. However, a simplification is possible by noting that thecomplementary operations of AtoD conversion performed in blocks 1306,1308 and mapping to a symbol performed by DtoA convertors 1310 and 1311simply cancel each other out and can be omitted in this alternateexemplary embodiment. Then, the full unquantized accuracy of the analogI and Q signals from the low pass filters is preserved through themultiplexers and the digital multiplexers are replaced with analogmultiplexers as shown in FIG. 15.

In FIG. 15, baseband signals are produced by downconvertors 1501, 1502and low pass filters 1503, 1504 as described above with respect to FIG.13. The I,Q signals are however no longer digitized and instead areapplied directly to the inputs of analog multiplexers 1505, 1506 alongwith corresponding signals from other antenna channels (not shown). Themultiplexed I samples then modulate a K-band cosine carrier and themultiplexed Q samples modulate a K-band sine carrier, by use ofquadrature modulator 1507. Spare inputs of the analog multiplexers, aspreviously indicated, can be used to multiplex and transmit referencevalues such as (0,0), (1,0) and (0,1) which can be helpful in assistingthe ground station receiver to acquire demultiplexor synchronization andin correcting certain errors in the quadrature modulator such as carrierimbalance (carrier leakage, offset) and imperfect quadrature (i.e., thecosine and sine carriers are not exactly 90 degrees apart).

The configuration illustrated in FIG. 15 has an advantage thatsubstantially no bandwidth expansion of the signal takes place from 2GHz to K-band. The N, 5 MHz wide antenna signals received at 2 GHz areretransmitted at K-band using substantially the same 5N MHz bandwidth.Furthermore, no quantization noise is introduced.

A suitable analog multiplexer for the exemplary embodiment of FIG. 15can be constructed as a binary tree, in which pairs of 5 MS/S signalsare first multiplexed in relatively low-speed, 2-input multiplexers toform 10 MS/S signals. Then pairs of these are multiplexed in higherspeed 2-input multiplexers to form 20 MS/S signals and so on. Themultiplexers can be constructed in a bipolar, CMOS or BiCMOS integratedcircuit using current steering in which a signal is applied to thejunction of two transistor inputs (e.g., emitters) that are alternatelyenabled or disabled by a control signal (applied, e.g., to bases) toeither pass the signal current through one of the devices or to shunt itaway through the other. Gallium arsenide technologies, such as HBT, arealso very suitable for constructing high speed multiplexers.

The ground station processing system receives the time-multiplexedantenna signals on K-band, converts those signals down to I,Q basebandsignals of 2.5N MHz bandwidth each, and then demultiplexes them into N,separate 2.5 MHz bandwidth signals of 5 MS/S each (the Nyquist rate orhigher). These signals can then be digitized on the ground to whateveraccuracy is required for further processing such as using an equalizerfor removing inter-sample interference on a sample caused by smearingfrom adjacent samples due to deliberate or accidental bandwidthrestrictions in the K-band transmitter, receiver or propagation path.Such an equalizer operates by subtracting a defined amount of a previousand subsequent complex (I,Q) sample value from a current value, thedefined amounts being given by complex coefficients that are chosen tocancel inter-sample interference. This process can also be applied inreverse for conveying to the satellite using K-band complex signalvector samples for transmission by respective antennas at, for example,S-band.

The N separate, complex (I,Q) sample streams are first preferablysubjected to pre-equalizing at the ground station such that they will bereceived with zero intersample interference at the satellite. Then thetime-multiplex modulated K-band signal is downconverted in the satelliteagainst a K-band local oscillator to give multiplexed I and Q streams.If desired, two or more stages of downconversion can be employed so thatamplification takes place at convenient intermediate frequencies. Thismay also apply to the 2 GHz downconverters of FIG. 13, but note that thesame local oscillator signals should then be employed in allcorresponding stages of downconversion for each antenna element so asnot to introduce relative phase shifts.

The multiplexed I,Q streams received by the satellite can bedemultiplexed using the same multiplex clock (not shown) used formultiplexers 1505 and 1506. The onus is thus on the ground station totransmit a signal taking into account propagation time such that thesignal will arrive in the correct timing relationship to ensure properdemultiplexing on board the satellite. In this way, the satellitefunction is kept simple and reliable and complexity is restricted to theground, where equipment can be repaired should it fail.

The above description has been simplified for purposes of illustrationto the case where all antenna element signals are time-multiplexed to asingle TDM complex sample stream. Those skilled in the art will readilyappreciate, however, that a hybrid TDM/FDM scheme could be used in whichgroups of time-multiplexed signals are formed and used to modulateseparate FDM carriers. This modification could be used if, for example,a single multiplex stream would result in an impractically high samplerate.

It is also for the purposes of illustration that the above descriptionhas concentrated on the Cartesian (I,Q) representation of complexsignals. It is equally possible to form polar or logpolarrepresentations of complex signals, to multiplex these signals usinganalog multiplexers prior to modulating a K-band feeder link or todigitize them using the method of U.S. Pat. No. 5,048,059, which wasearlier incorporated by reference, prior to multiplexing.

FIG. 16 shows transmit signal processing in the hubstation for thisexemplary embodiment of the present invention. Each voice channel to betransmitted to a mobile phone can be received either as a standard 64KB/s PCM signal or as an analog signal which is converted to PCM. ThePCM signal is then transcoded to a lower bit rate, such as 4.8 KB/s,using a conventional voice compression algorithm such as CELP (codebookexcited linear prediction), RELP, VSELP or sub-band coding. Thetranscoded voice signal is then subject to error correction coding andsupplementary bits can be added such as the Cyclic Redundancy Check bits(CRC), Slow Associated Control Channel signalling information (SACCH),per-slot syncwords and inter-slot guard symbols. This per-channelprocessing takes place in voice processing channel cards 1600. Theoutput bitstreams from, for example, 500 such channel cards, are thenmultiplexed with a control channel data stream from a control processor(not shown) in multiplexer 1601 to form the TDMA bitstream, for example,of 6.5536 megabits per second. This is submitted to a digital modulator1602 that numerically converts the information stream to a stream ofcomplex numbers at a sample rate of, for example, eight samples per bitrepresenting the I, Q components of a modulation waveform.

The TDMA signal produced as described above is targeted for transmissionto a first set of, for example, 500 mobile phones in a particular cellor area. A number of other such TDMA signals formed by similar circuitry1600, 1601, 1602 are produced for transmission to other sets of 500mobile phones in 36 other cells. The total number of cells (e.g., 37 inthis exemplary embodiment) times the number of traffic channels per cell(e.g., 500) gives the total system capacity as 18500 voice channels. Thesignals in timeslots 1 of each cell are transmitted simultaneously onthe same frequency to their respective cells. To avoid spilloverinterference from adjacent cells using the same frequency at the sametime, this exemplary embodiment of the present invention includes matrixprocessor 1603 to process the signals from modulators 1602 by weightedaddition using a matrix of 37×37 complex coefficients for each timeslot.The 37×37 coefficients for each timeslot are contained in coefficientmemory 1605 which can be distributed within the components of thenumerical signal processor but which is collectively identified as aseparate block 1605 in FIG. 16 to better illustrate the principle.During the first timeslot, a first set of coefficients C is selectedfrom the memory and used to matrix-multiply the modulation signals frommodulator 1602 to obtain signals for D/A convertors 1604. Each D/Aconvertor can be a dual-channel unit capable of operating with complexnumbers. For example, the output signals from the matrix processor canconsist each of a 12-bit real (I) and 12-bit imaginary (Q) part whichare D/A converted to produce analog I, Q signals. The I, Q signals arefed to FM K-band FM transmitters for transmission from the hubstation tothe satellite.

When transponded by the satellite to the ground on S-band, the result ofthe matrix processing will be that each mobile phone receives only itsown signal, the inter-cell interference from other cells having beencancelled by the addition in the matrix processor of compensatingamounts of opposite sign as determined by the coefficients retrievedfrom memory 1605. This is possible if the 37 mobiles using timeslot 1 intheir respective cells are spatially separated, i.e., not both at thesame location on the edge of their respective cells. This condition canbe maintained by the exemplary timeslot assignment algorithm feature ofthe present invention, which also provides a general channel assignmentalgorithm, and is based on maximizing the signal quality provided to theworst case mobile.

A timeslot duration is typically about 40 μS if a 20 mS TDMA frameperiod is used. One timeslot corresponds to 256 bit periods at 6.5536MB/s and 2048 complex numbers are produced by modulator 1602 for everytimeslot. After matrix processor 1603 has processed 2048 sets of 37complex number inputs using the set of coefficients for the firsttimeslot, the coefficients are changed for the second and for subsequenttimeslots to effect correct interference cancellation betweencorresponding sets of 37 mobiles using timeslots 2, 3 etc.

If two mobiles receiving the same timeslot in different cells approacheach other too closely during the progress of a conversation, thecontrol processor (not shown) will note a difficulty in arriving at asuitable set of coefficients for interference cancellation. This ishighly unlikely given the limited speed of landmobile phones in relationto typical cell size, but if it occurs, the control processor evaluateswhether a timeslot change would be appropriate for one of the mobiles.The aim is to connect the mobile using a timeslot that no other mobilein close proximity is using. If necessary, a mobile even occupying anideal (e.g., low interference) timeslot could be shifted to a justadequate (e.g., barely tolerable interference) timeslot to release itsoriginal timeslot to solve a proximity problem at hand. It is probablynot necessary in practice to consider such a situation because with, forexample, 500 timeslots to choose from, it would usually be possible tofind a better timeslot than the timeslot currently threatening to causebad signal quality. Allowing one timeslot change per cell per 10seconds, for example, would be expected to achieve adequately rapidoptimization of timeslot assignments and adequate adaptation to mobilemovement.

In fact a more rapid rate of adaptation is provided to handle the rateat which new calls are placed and old calls cleared down. With acapacity of 37 mobiles per timeslot and an average call duration of 3minutes, a particular timeslot is vacated in some cell approximatelyevery 5 seconds and a new call is then assigned to that timeslot.Overall, given, in this example, 500 timeslots and 37 cells, 100timeslots spread over all the cells are vacated every second andreassigned.

Such a communications system should be designed to not be loaded up to100% of system capacity or the next call attempt will be blocked. With500 timeslots per cell available, an average loading of 474 timeslotscan be reached for a blocking probability of 1%. Thus, on average, 26out of 500 timeslots are unused on each of the 37 multiplexers 1302 inthis exemplary embodiment. It should be noted that it is immaterialwhich multiplexer is used to transmit a particular timeslot to a mobile.Whichever timeslot is selected, it is the choice of an associated columnof matrix coefficients that determines that mobiles using the sametimeslot are non-interfering. Thus if the same timeslot, for examplenumber 371, is vacant on two or more multiplexers 1601, it is immaterialwhich one is used to connect a new call.

Thus the assignment algorithm executed in the control processor firstdetermines which timeslot is vacant on the greatest number ofmultiplexers. This is the timeslot on which there are currently theleast number of mobile conversations. Using information from the randomaccess receiver on the relationships between signals received from thenew mobile (i.e., the C-matrix coefficients determined by correlation ofthe new mobile's random access signal with all antenna element signals),the control processor evaluates the change needed to the set ofcoefficients in coefficient memory 1605 associated with the vacanttimeslot to maintain non-interference if that timeslot were to be usedfor the new signal.

The general principles that explain how the choice of coefficients incoefficient memory 1605 is arrived at for an exemplary embodiment willnow be outlined.

As discussed earlier, for receiving signals from mobiles, antennaelement 1 received an amount C11 of mobile signal M1 plus an amount C12of mobile signal M2 and so on. To state this more generally, antennaelement k received an amount Cki of mobile i's signal. Assumingreciprocity, a signal Tk transmitted from antenna element k would bereceived in an amount Cki. Tk at mobile i, because the path from elementk to mobile i is assumed to have the same attenuation and phase shift ineach direction, given by the complex number Cki.

Therefore the signals R received at the mobiles are related to thesignals transmitted by the antenna elements by the matrix equations:

    R=C.sup.t.T; where the superscript t indicates a transpose matrix.

The transpose of C is used because the first index k of Cki multipliesthe corresponding index of the T-element, while, in themobile-to-satellite direction where the signals received at element kfrom mobile i are given by Cki.Mi, it is the second index i of C whichcorresponds to the index i of the mobile signal Mi that it multiplies.Thus the indices of the matrix coefficients are transposed in thesatellite-to-mobile direction as compared to the mobile-to-satellite.

In order to achieve non-interference, the set of signals transmittedfrom the satellite antenna elements should be given by:

    T=C.sup.t-1.R

The inverse of the transpose is just the transpose of the inverse,therefore the set of coefficients contained in coefficient memory 1605for downlink timeslot(j) are just the transpose of the set ofcoefficients associated with uplink-frequency(j) in numerical processor650 of FIG. 9, at least under the assumption of reciprocity.

Reciprocity applies when the uplink and downlink frequencies are thesame. Relative amplitude reciprocity applies if the antenna elementpatterns are the same on both uplink and downlink frequencies. Phasereciprocity does not apply, because relative phase depends on the smalldifferences in relative distance travelled by the signals to/from eachelement, divided by the wavelength and multiplied by 360 degrees. If thewavelength is different on the uplinks and downlinks, then the phaserelationships will be different. However, relative time delaydifferences are frequency independent and therefore reciprocal.Accordingly, a set of relative phase differences at one frequency can betranslated to a set of time differences using a first wavelength, andthen reconverted to a set of phase differences using another wavelengthin order to derive a set of coefficients valid at a second frequencyfrom a set known at a first frequency.

Based on the foregoing discussion, the coefficients for transmitcontained in memory 1605 according to an exemplary embodiment of thepresent invention can be determined by the following steps:

(1) correlating the signal received from a new mobile during its randomaccess transmission with the individual antenna beam element signals todetermine a new column of coefficients for the receive C-matrix;

(2) determining a new inverse C-matrix for receiving traffic from thenew mobile based on the old inverse C-matrix and the new column;

(3) transforming the new receive C-matrix column to a new transmitC-matrix row by scaling relative coefficient phase angles using theratio of up- to down-link frequencies; and

(4) determining a new transmit inverse C-matrix based on the oldtransmit inverse C-matrix and the new row.

An exemplary detailed mathematical procedure which can be used to carryout the above exemplary embodiment is now developed for the underloadedcase, i.e., the case when there are fewer currently active mobilesignals than the number of antenna feed elements available on thesatellite to communicate with them. Such spare capacity is typicallydesigned for in radio telecommunications to provide a 98% probability ofhaving a free channel to serve a new call so that customers are notoverly irritated at call blockages.

The active mobiles are designated 1 . . . m and the signals intended tobe received by these mobiles are designated R1 . . . Rm for thisexample. The antenna element/transponder channels available forcommunications therebetween are designated 1 . . . n and the signals fedto the antenna elements for transmission by each respective element aredesignated T1 . . . Tn. As before, the matrix C, this time an m×nnon-square matrix, determines how much of each transmitted signal Tkreaches each mobile as Ri, the matrix is given by the equations:##EQU2## or simply R=C.T in matrix/vector notation.

Because C is no longer square, it has no direct inverse, so there is nounique solution for T given by:

    T=C.sup.-1.R

Instead there are a continuum of solutions, as we have more degrees offreedom to choose T values than conditions to satisfy (i.e., n>m).

However by imposing the condition that the mean square power fed to theantenna elements in order to create the desired mobile received signalsR shall be minimized, the unique solution below is obtained:

    T=C.sup.t.(CC.sup.t).sup.-1

This equation can be derived as follows. Let R_(desired) be theM-element vector of signals we wish to be received at the receivingstations, and T be the N-element vector of signals applied to thetransmitting antennas, where N>M. C is an M by N matrix of coefficientsCik that describes how the signal from transmitter antenna j propagatesto receiving station i. Denoting by R_(achieved) the M-element vector ofsignals actually received, we thus have

    R.sub.achieved =C.T                                        (1)

We wish to find what T should be as a linear function of the signalsdesired to be received, so that the minimum total transmit power isconsumed in the process. The linear combinations formed by thecoefficients of an M by N matrix A to be found are:

    T=A.R.sub.desired                                          (2)

Substituting for T from (2) into (1) we get:

    R.sub.achieved =C.A.R.sub.desired

showing that R_(achieved) =R_(desired) only if C.A is the M×M unitmatrix I

    Thus C.A=I                                                 (3)

is a necessary condition. Since C is not square, we cannot simply invertit and write:

    A=C.sup.-1

Moreover, C.A.=I is a set of M×M equations that the N×M unknowns A mustfulfill so that the M×M terms of the product indeed give the M×M unitmatrix I.

Since N>M, the number of unknowns is greater than the number ofequations, so there is no unique solution to equation (3), but acontinuum of solutions. Other conditions must be imposed to define aparticular solution of interest. The condition imposed here is that thetotal power inherent in transmitting the vector of signals T isminimized.

It can be verified that a particular solution of equation (3) isA=C'(CC')⁻¹ =U, where ' signifies conjugate transpose. This can beverified by substituting the particular solution U for A in equation(3), obtaining:

    C.U=C.C'(CC').sup.-1 =(CC')(CC').sup.-1

, which is clearly equal to I as required.

A general solution can be formed by adding an arbitrary matrix V to theparticular solution found above, obtaining:

A=C'(CC')⁻¹ +V, but this must still fulfill equation (3).

Substituting this value of A into equation (3) we get:

    C(C'(CC').sup.-1 +V)=I

    i.e., CC'(CC')+CV=I

    i.e., I+CV=I

    i.e., CV=0                                                 (4)

Thus, V may be arbitrary only so long as it fulfills equation (4). It ispossible for a non-zero V matrix to give identically zero whenpremultiplied by C as long as all V's columns are orthogonal to all C'srows. The rows of C are N-element vectors, but there are only M of them,therefore they do not totally span their N-dimensional space. There areN-M other dimensions in that space that the rows of C do not projectinto, and the columns of V may thus consist of any vectors that areconfined to that N-M dimensional sub-space that do not project into C'sM-dimensional sub-space.

Thus, the general solution of equation (3) is

    A=U+V; where U is the particular solution identified above and V must satisfy C.V=0 ##EQU3## where R1, R2, etc. are the elements of R.sub.desired. If R1, R2, etc. are all independent signals intended for different receiving stations, there is no correlation between them so they add rms-wise in the linear summing process that forms the T-elements.

Thus, the mean square value of T1 is just |A11.R1|² +|A12.R2|² . . .+|A1m.Rm|²

Likewise, the mean square value of T2 is |A21.R1|² +|A22.R2|² . . .+|A2m.Rm|²

Adding these expressions down columns that contain the same Ri, we get:

    POWER=SIGMA.sub.j  |Ri|.sup.2.SIGMA.sub.i |Aij|.sup.2 !

Now SIGMA^(i) |Aij|² =SIGMA_(i) (Aij.Aij)=SIGMA_(i) (A'ji.Aij), whereA'ji refers to element ji in the conjugate transpose of A.

But this value SIGMA is simply the jj diagonal term of the whole matrixproduct Xjk=SIGMA_(i) (A'ji.Aik), which is the equation for matrixmultiplying A'and A, i.e., X=A'A.

Now substitute A=U+V; then:

X=(U'+V').(U+V)=U'U+V'V+U'V+V'U and

U'V+V'U=2Re (U'V).

Substituting U=C'(CC')⁻¹, i.e., U'=(CC')⁻¹.C, into the foregoingequation, we get U'V=(CC')⁻¹.CV=0 because CV=O.

Therefore 2Re(U'V)=0 and U'V+V'U=0.

Hence SIGMA_(i) |Aij|² =SIGMA_(i) (|Uij|² +|Vij|²), leading to:

    POWER=SIGMA.sub.j  |Ri|.sup.2. SIGMA.sub.i |Uij|.sup.2 !+SIGMA.sub.j  |Ri|.sup.2. SIGMA.sub.i |Vij|.sup.2 !

Since the two terms involving respectively U and V can only be positive,the power is minimized when the choice of the arbitrary matrix V in thesecond term is zero. Hence, the solution for the transmit signals thatcreate the desired received signals is:

    T=A.R.sub.desired where A=C'(CC').sup.-1

This solution also holds for the case where N=M, for then C is squareand the above reduces to:

    A=C.sup.-1

Applying the foregoing principles, the spare degrees of freedom are usednot just to create co-channel interference free signals at every mobile,but also to maximize the wanted signal values for a given total radiatedpower. The total mean square radiated power is in fact the sum of thesquare magnitudes of the coefficients of the matrix A defined by:

    A=C..sup.t (C.C).sup.-1

The sum of the squares down a column of A gives the radiated power usedin communicating with a corresponding mobile. The worst case mobile,i.e., that using the most satellite power, can thus be identified.According to an aspect of the present invention, the control processorat the hubstation periodically examines whether total satellite powercan be minimized (or utilization of power optimized) by removing theworst case mobile from the current group the mobile is associated withand associating that mobile with a different group. This is done byrecomputing the above expressions with C diminished by the rowcorresponding to the worst case mobile, thus determining the satellitepower saving that would be saved in supporting only the remainder in themost efficient manner. Then the removed row of C is used to augment inturn each of the C matrices associated with other groups of mobilesusing different frequency channels (FDMA) or multi-carrier (CDMA) ortimeslots (TDMA) and the above expressions computed to determine theincrease in power that would be necessary to support that mobile as amember of each of the other groups in turn. If the increase in power inone of these cases is less than the power saved by removing the mobilefrom its original group, then a frequency or timeslot handover to thenew group can be performed in order to improve satellite powerutilization. This procedure can likewise be used for determining whichof a number of existing groups a new mobile call should be associatedwith, i.e., to find the group that would result in minimum increase ofsatellite power used when a new call is connected.

FIG. 17 shows an exemplary embodiment illustrating the interconnectionsbetween the transmit and receive matrix processors and the controlprocessor at the ground station to effect the above-describedinterference cancelling and optimum channel allocation behavior.

The receive matrix processor 1700 receives digitized signal samples fromthe ground station RF section. The receive processing can be structured,for example, according to the exemplary FDMA embodiment of the inventionof FIG. 9, or according to the exemplary TDMA embodiment of FIG. 16.Moreover, an exemplary CDMA embodiment can be constructed by, forexample, increasing the bandwidth of the channel splitting filters andincluding a CDMA version of the per-channel processing in the circuitryof FIG. 9. Further, exemplary embodiments of the present invention maybe constructed using the novel subtractive CDMA system described in U.S.Pat. No. 5,151,919 to Paul W. Dent entitled "CDMA SubtractiveDemodulation", which is incorporated here by reference. These featuresof the present invention also lend themselves to implementation inland-based cellular systems.

The receive matrix processor 1700 separates the individual channelsignals by applying inverse C-matrix coefficients supplied by controlprocessor 1702 as described above, to eliminate or suppress co-channelinterference. These coefficients can, for example, be determined asfollows.

When M spatially separated antenna/receiver channels receive differentcombinations Ri of M signals Si, given by

    Ri=SIGMA.sub.j (Cij.Sj)                                    (5)

or in matrix notation, R=C.S, then the separation of the M signals has astraightforward solution

    R=C.S.sup.-1                                               (6)

When the number of antenna/receiver channels N is greater than thenumber of signals M they receive, the matrix C is not square and cannotbe inverted. There are a continuum of solutions possible using anysubset M of the N channels, but there can also be a desired uniquesolution.

The reciprocal problem for transmitting M signals using N transmitterchannels was solved above by imposing the additional desire to minimizetotal transmit power. In the receiving case, we can find the desiredunique solution by imposing the condition of maximizing the signal tonoise ratio. To do this, a finite amount of noise must be assumed toexist in the receivers.

Before this solution is described, another solution will be describedfor solving the equations: ##EQU4##

When N>M there is an excess of equations over unknowns. They should allbe consistent and solving any subset M of N should yield the sameanswer. Due to receiver noise, however, which causes uncorrelated errorsin the received values R, the equations will not all be exactlyconsistent.

A known solution to this is the so-called least-squares solution. Theleast squares method seeks the solution which nminimizes the RMS sum ofthe noise errors needed to be added to the R-values to make theequations consistent.

An error vector E may be defined as

    E=C.S-R                                                    (8)

The sum square error is then

    E'E=(C.S-R)'.(C.S-R)=S'.C'.C.S-R'.C.S-S'.C'.R+R'.R         (9)

Differentiating this expression with respect to each R value to obtainthe gradient yields:

    grad(E'E)=2C'.C.S-2C'.R                                    (10)

E'E is a global maximum where grad(E'E)=0,

    i.e, C'C.S=C'R, or S=(C'C).sup.-1.C'.R                     (11)

The least squares solution for the M signals is thus S=A.R where

    A=(C'C).sup.-1.C'                                          (12)

This may be compared with the least-power transmit solution where

    A=C'(CC').sup.-1

The least squares solution for reception given above is not necessarilythat which maximizes the quality of each signal. To find the solutionthat maximizes each signal quality we in turn find the best A matrix rowthat yields that signal.

Separated signal Si is given by row i of A, henceforth written Ai,multiplied by the vector of receive channel outputs R, i.e., Si=Ai.R. Ris given by C.S+Noise where "Noise" is a vector of uncorrelated noisehaving components N1,N2 . . . in the receiver channels.

Thus

    Si=Ai.C.S+Ai.Noise                                         (13)

The amount of wanted component Si that appears in Si is given by

(Ai1.C1i+Ai2.C2i+Ai3.C3i . . . +AiN.CNi).Si=Ai.Ci where Ci means the ithcolumn of C.

Assuming all Si are transmitted with unit power, the power in theextracted wanted component is

    P=|Ai.Ci|.sup.2 =Ai.Ci.Ci'.Ai'           (14)

There are also, however, unwanted components in the extracted signal dueto the other signals Sk. The sum of the unwanted powers for all k notequal to i is given by

    I=Ai.Cdim.C'dim.Ai'                                        (15)

where Cdim means the matrix C with column i removed. In addition, thereis a noise power given by

    |Ai1.N1|.sup.2 +|Ai2.N2|.sup.2 . . . =AiAi'.nI                                                 (16)

where n is the mean square value of each of the noise signals N1,N2,etc. The signal-to-noise-plus interference ratio is then given by##EQU5## Mathematicians will recognize this expression as the ratio ofHermitian forms. The maxima and minima of such expressions as

    x'ux /x'vx

are given by the eigenvalues q of V.⁻¹ U, i.e., by the solution ofdet(V⁻¹.U-qI)=0. The values of X which give these extrema are thecorresponding eigenvectors. V.⁻¹ U in our case is(Cdim.C'dim+nI)⁻¹.Ci.Ci' and X is A'.

We now use the theorem that the eigenvalues of the product of an n by mmatrix with an m by n matrix where n>m are equal to the eigenvalues ofthe product taken in reverse order, plus n-m zero eigenvalues.

Using as the two matrices in question the N by 1 matrix(Cdim.Cdim'+nI)⁻¹.Ci on the one hand and the 1 by N matrix Ci' on theother hand, the eigenvalues we need must be those of the inverse product##EQU6## This, however, has dimension 1×1, i.e., it is a scalar, so ithas only one non-zero eigenvalue.

    Hence q=Ci'.(Cdim.C'dim+nI).sup.-1.Ci                      (19)

The associated eigenvector Ai' is the solution V of an equation of theform

    Matrix.V=V.Eigenvalue

    (Cdim.C'dim+nI).sup.-1.Ci.Ci'.V=Vq                         (20)

Substituting for q from equation (19),

    (Cdim.C'dim+nI).sup.-1.Ci.Ci'.V=V.Ci'.(Cdim.C'dim+nI).sup.-1.Ci(21)

It may be verified that letting V=(Cdim.C'dim+nI)⁻¹.Ci makes the righthand and left hand sides of equation (21) identical. Thus, thiseigenvector is the optimum solution for the row of coefficients Ai thatextract Si from R with best signal-to-noise+interference ratio.

If instead we set out to maximize signal to

(signal+noise+interference) ratio we would get

    Ai'=(C.C'+nI).sup.-1.Ci or Ai=Ci'.(C.C'+nI).sup.-1         (22)

i.e., the whole C-matrix is used in the inversion and not Cdim with onecolumn removed. The value that maximizes S(S+N+I) should, however, bethe same as that which maximizes (S/(N+I) as their reciprocals differ bythe constant 1 only.

It can be shown that this solution only differs by a scalar factor1/(1+q) from the solution which maximizes S/(N+I), and since a fixedscaling does not change signal to noise ratios, it is effectively thesame solution. If such Ai's are now derived for all i and laid one underone another to form an M by N matrix A, the rows Ci', being the originalcolumns Ci, also lie under one another to form the matrix C'.

Thus A=C'(CC'+nI)⁻¹

This is similar to the solution for minimum transmit power derivedabove, except that the "C" matrix here is the transpose of the transmitmatrix and is M by N instead of N by M. That means that N×N matrix CC'has rank of only M<N and it has no direct inverse, being singular.However, the addition of the noise down the diagonal through the term nIis the catalyst that makes the matrix to be inverted non-singular andthe above solution computable.

The solution in the transmit case provided a way to test how much thetotal transmit power, having been reoptimized, would have to increase tosupport one extra signal. Reciprocally, in the receive case, it can betested how the addition of a new signal to those already received wouldaffect the signal to noise ratio after re-optimization of the abovecoefficients with an extra column added to the C matrix. The extracolumn of C's in question represents the relative strengths and phaseswhich the new signal is received by the N receiver/antenna channels.This is determined while the new signal is appearing on the randomaccess channel and not in conflict with other signals. Furthermore,random access can be made with higher power or more coding than fornormal traffic so as to facilitate detection and decoding.

The signal is decoded and retrospectively the decoded signal can becorrelated with signal samples recorded from each of the N channels todetermine the new C-matrix coefficients. A test is then made byappending the new C column to each of a number of candidate C matricesin turn associated with different groups of ongoing signals in order todetermine the group that would have its worst case SNR degraded theleast by inclusion of the new signal. This then determines theallocation of a channel to the new signal for traffic, and explains howthe C matrix coefficients are arrived at a row-at-a-time during therandom access and channel allocation process.

The separated channel signals are processed in separate channelprocessors 1701. The channel processors can either be engaged to processsubscriber traffic, after a call has been connected, or can be employedto search for random access signals from a given direction. The latteris done by combining the received signals from the satellite to formbeams covering fixed regions of the earth from which random accesssignals may be received. The coefficients used may be chosen by thecontrol processor 1702 to provide cancellation or reduction ofinterference from other signals on the same frequency from other regionsso as to maximize the probability of intercepting a random accessmessage. The random access message can also be provided with anadditional degree of error correction coding to maximize receptionprobability in the absence of a-priori knowledge of the direction fromwhich an access attempt is received. Optionally, the random accesschannel can be frequency-planned to avoid immediate frequency re-use inadjacent cells, for example by the use of a 3-cell frequency or timeslotre-use plan, since using three frequencies or timeslots for randomaccess does not have such a deleterious effect on total system capacityas if such a frequency usage plan were adopted for every trafficchannel.

The channel processors 1701 provide information to the control processor1702 regarding the amount of each signal in each beam channel orseparated channel, which the control processor 1702 uses to control theinterference cancellation coefficients used by the receive matrixprocessor 1700. Depending on, for example, the determinationrespectively of correlations between each separated signal and each beamsignal or the determination of correlations between separated signals,two different control concepts can be applied by control processor 1702.

In a first exemplary control implementation, a separated channel signaldecoded by a channel processor 1701 is correlated or partiallycorrelated with each non-separated beam signal in turn. The electricalconnections for achieving this correlation are disposed between everychannel processor 1701 and every other channel processor 1701, howeverthese connections are omitted from FIG. 17 for clarity. The part of theseparated signal that is used for correlation can suitably be a knownbit pattern in the channel signals, for example a synchronization wordor bit pattern. The correlation results directly represent the C-matrixcoefficients and these are processed by the control processor to obtainA-matrix coefficients as defined above.

In a second exemplary control implementation, a separated channel signaldecoded by a channel processor 1701 is correlated with at least part ofother channel signals to determine the residual amount of non-cancelledinterference present due to other channel signals. That part of theother channel signals with which correlation is performed can suitablybe a known pattern contained in each signal, such as a synchronizationword. Since these patterns are known it is not necessary to cross-couplethe channel processors 1701 to each other, thus avoiding a mass ofinterconnections. Furthermore, since adaptation of the receive matrixcoefficients by the control processor 1702 does not have to take placeat a rapid rate, as they are relatively static for a given set oftransmitting mobile phones, the correlation with different signals canoccur at different times at which the transmitters, by prearrangement,insert a special sync word for the purpose of correlation.

For example, suppose a known, 16-bit sync pattern is employed withineach segment of transmitted signal, e.g., a TDMA timeslot. There are 16possible orthogonal 16-bit words, so 16 different signals can beallocated orthogonal sync words. A Fast Walsh Transformer such as theone described in U.S patent application Ser. No. 07/735,805 entitled"Fast Walsh Transform Processor" and filed on Jul. 25, 1991, which isincorporated here by reference, provides an efficient means to correlatea signal simultaneously with all possible orthogonal codewords and thusdirectly determine the residual, non-cancelled interference amounts. Ifhowever the number of signals whose residual interference contributionsare to be discriminated is greater than 16, for example 37, then 15 at atime can be arranged to use different orthogonal codewords while theother 22 use the 16th codeword. The 15 which are chosen to use differentcodewords can be changed between successive TDMA frames such that afterslightly over two frames all signals have been uniquely discriminated.

This exemplary procedure can also be applied to FDMA or CDMA uplinkmodulations. In the CDMA case, for example, orthogonal spreading codescan be allocated to facilitate discrimination. If a hybrid FDMA/CDMAuplink is used with, for example, four overlapping, orthogonal CDMAsignals on each frequency channel as described in the aforementioneddisclosure, U.S. Pat. No. 5,539,730, entitled "TDMA/FDMA/CDMA HybridRadio Access Methods" granted Jul. 23, 1996 then the system can readilysearch simultaneously for known sync patterns employing all fourorthogonal codes. By permuting the underlying sync patterns as describedabove, it is possible to discriminate residual interferencecontributions from any number of different CDMA transmissions using thesame channel frequencies at different locations. This can beaccomplished, for example, after separating the signals using theC-matrix, a signal can be correlated with its own known bit pattern andthe known patterns of other signals that should have been cancelled;results of the latter correlations yield the amount of residual,uncancelled signal and can be used to update the C-matrix.

In this second exemplary implementation, C-matrix coefficients are notdirectly determined, but rather the residual interference amounts arerelated to errors in the A- and C-matrix coefficients. This relationshipcan be demonstrated as follows.

The satellite or base station broadcasts N combinations of M desiredsignals from N transmitter/antennas. The N combinations should be chosensuch that each of the receiving stations receives only its intendedsignal, and the other M-1 at that receiver are cancelled. The N linearcombinations are preferably those derived as set forth above, whichresult in each receiving station receiving its intended signal only, andwith minimum total transmitter power.

The transmitted signals ##EQU7## are formed from the signals desired tobe received ##EQU8## by multiplying the vector Rd by the N by M matrixA, i.e., T=A.Rd.

A is in turn shown above to be preferably equal to C'(CC')⁻¹ where Cijis the propagation from transmitter/antenna j to receiver i. Estimatesof Cij are made at call set-up time for the receive direction andtransformed to estimates for the transmit direction as described above.There will, however, be errors in the estimates of the Cij for thetransmit direction that are used to compute the matrix A. Let us assumethat the estimated transmit matrix C is equal to the true matrix Co plusan error matrix dC, i.e.,

    C=Co+dC or Co=C-dC

The signals Ra actually received by the receiving stations are given bythe true C-matrix Co times the transmitted signals, i.e.,

    Ra=Co.T=Co.A.Rd=(C-dC)C'(CC').sup.-1.Rd=Rd-dcC.C'(CC').sup.-1.Rd=Rd-dC.A.Rd

The errors dR in the received signals dR=Rd-Ra are thus given by

    dR=dC.A.Rd                                                 (23)

Each error element i of the error vector dR contains a part e_(ij) ofeach of the other unintended signals j.

If the M signals contain known signals, patterns or syncwords, bycorrelating with these at a mobile receiving signal i, it is possible todetermnine the residual unwanted amount of signal j, and thus determinee_(ij).

The syncwords can be orthogonal so that correlation with all of them canbe performed at the same time by means of an orthogonal transform suchas the Walsh-Hadamard transform. If the number of orthogonal codewordsavailable is less than the number of signals M, the orthogonal codewordscan be assigned to groups of immediately surrounding beams or cellswhose signals are most likely to interfere due to imperfectcancellation. A limit set of orthogonal codewords can be permutedbetween the M signals to allow different subsets to be resolved at atime, and all M to be resolved sequentially. In this way, by correlatingthe received signals Ra over the portion containing the known signalpattern with all orthogonal codewords the amount of own codeword isobtained as well as the amount of unwanted codewords. The amount ofother codewords is scaled by dividing by the complex amount of owncodeword correlation to yield the normalized error residuals e_(ij) thatmay then be complex-value averaged over several measurement intervalsbefore being reported by the receiving stations back to the transmittingstations on a reverse Slow Associated Control Channel. To reduce thevolume of reporting, each mobile can at each interval restrict itself toreporting only the largest error its correlator determines. Thetransmitting station can optionally either assume that the other errorsare zero at that station, or that they are as previously reported if noaction to correct them has been taken in the meantime.

The matrix E=e_(ij) may thus be equated to the matrix dC.A in (23), sowe have dC.A=E or A'.dC'=E'.

This is an insufficient set of equations for the unknowns dC', but aunique solution exists for which the sum of the squares of the dC's isleast, that solution being

    dC'=A(A'A).sup.-1.E'

Moreover, if A=C'(CC')⁻¹ then A(A'A)⁻¹ =C', therefore dC'=C'.E' or

dC=E.C Thus, given the original estimate of C and the residualcorrelation measurements reported by receiving stations, the error dC inthe original estimate may be calculated and the estimate of C graduallyrefined.

As mentioned above, if the reverse SACCH signalling capacity does notallow all errors to be reported every time, it is sufficient to reportonly the largest. The transmitter can choose only to correct the largestthere and then, or to wait until others are reported. In order to ensurethat others are reported, the transmitter can request the receiver tomake specific measurements via the forward SACCH channel. Theserefinements are mentioned for the sake of completeness in describing thescope of the invention, but the extra complexity is probably not neededin a satellite-mobile communications system where the relative positionsof mobiles in the satellite beams changes only slowly relative to thespeed of communications.

The control processor obtains initial estimates of the downlink C and Amatrix coefficients, measured on the uplink by syncword correlation asdescribed earlier, to the downlink frequency. The control processor thencontinually outputs corrected A-matrix coefficients suitably translatedto the downlink frequency as described above to transmit matrixprocessor 1704.

A complication can arise in performing this translation due to phasemismatches between each antenna element channel. It was stated abovethat the relative amplitude between signals on the uplink and downlinkfrequencies could reasonably be considered to be the same, and that therelative phase between signals can be scaled by the ratio of up- anddownlink wavelengths. However, consider the case where phase mismatchesexist between the channels that relay the mobile-satellite uplinksignals from each antenna element. The signal phases are then not justantenna element phases, PHI(i), but contain the additive mismatch terms,dPHI(i). If PHI(i)+dPHI(i) is then scaled by the ratio of wavelengths,the PHI(i) part will scale correctly but the mismatch part dPHI(i) willnot because there is no correlation between phase mismatches on the up-and downlink paths. If the up- and downlink phase mismatches are denotedrespectively by uPHI(i) and dPHI(i) then we need to calculate:

a.(PHI(i)-uPHI(i))+dPHI(i)) ; where a is the wavelength ratio.

This can be written a.PHI(i)+(dPHI(i)-a.uPHI(i)) and the termdPHI(i)-a.uPHI(i), which is at least a single constant, has to bedetermined in some way to translate the A- or C-matrix coefficientsdetermined from receiving mobile signals to the coefficients that shallbe used for transmitting to the mobiles. This can, for example, be doneby a fixed system calibration that is carried out with the help of a fewmonitoring stations or "dummy mobiles" located at different positionsthroughout the service area. Alternatively, by having the mobiles alsomeasure a limited number of residual correlations with signals otherthan their own, and report these correlations on the slow associatedcontrol channel (SACCH), the system can receive enough information toperform the necessary calibrations for phase mismatch continuously. Suchreported information can also facilitate calibrating out amplitudemismatches if required.

The present invention can also be employed to improve the capacity oflandbased cellular radiotelephone systems. Such systems generally employ3-sector antennas to illuminate three adjacent cells from the same site,as described above. Because isolation between sectors is not high (infact isolation is almost zero for a mobile on the border of twosectors), it is not possible with conventional systems to permit use ofthe same frequency channel in all three sectors. According to exemplaryembodiments of the present invention, however, the same channel canlikely be employed as many times as there are antenna elements to formsectors. Thus a three-sector antenna (typically formed by three verticalcollinear stacks of dipoles in a corner reflector) provides theopportunity to re-use the same channel three times.

Land-based cellular communication capacity is limited by the parameterof carrier to co-channel interference ratio (C/I). The C/I which wouldbe obtained if signals on the same frequency are radiated around 360degrees of azimuth is the same as the C/I which would be obtained withcentrally illuminated cells. A 3-cell cluster or site then becomes theequivalent of a centrally illuminated cell as regards the re-use patternneeded to achieve a given C/I. It is known that a 21-cell re-use patternis needed to provide the required C/I in the AMPS system, therefore a21-site re-use pattern would be needed if all sectors in the same siteused the same frequencies over. This compares with the 7-site, 3-sectorpattern employed conventionally, showing that what has been gained fromusing the same frequency in every sector has been lost by the need toincrease the re-use pattern size from 7 sites to 21 sites. Thus,according to this exemplary embodiment of the present invention three ormore sectors or antenna elements around the 360 degrees of azimuthshould be used.

FIG. 18 shows an exemplary cylindrical array of slot antennas 1800suitable for implementing the present invention in landbased cellularsystems. The array consists of rings of eight slots around a metalliccylinder. Horizontal slot antennas give the desired verticalpolarization, and the slots are a half wavelength long, e.g.,approximately 16 centimeters for the 900 MHz band. It can be desirableto employ alternatively circular polarization at the base stationcombined with linear polarization at the mobile phone, especially whenthe mobile is a hand portable of uncertain antenna orientation. Circularpolarization can be formed by using crossed slots, crossed dipoles or ahybrid slot-dipole combination for the array elements. It is oftenconvenient when using such structures to form both polarizationssimultaneously, and this can be exploited by using opposite circularpolarizations for transmitting and receiving to reduce transmit-receivecoupling.

Element spacing around the cylinder must be somewhat greater than a halfwavelength to avoid the slots from running into each other, although itis possible to stagger alternate slots by a small vertical displacementto reduce their potential mechanical interference or electrical couplingwith each other. If, for example, 0.75 wavelength spacing is used, thencylinder circumference is 6 wavelengths, that is a cylinder radius ofless than one wavelength or about one foot. Such an antenna isconsiderably smaller than conventional three sector antennas. A numberof rings of such slots are stacked vertically with between, for example,0.5 and one wavelength vertical spacing to provide the same verticalaperture and, therefore vertical directivity, as conventional cellularbase station antennas. Slots that lie in a vertical column can beconnected by feedlines 1801 that feed them in phase. The eight feedlinescorresponding to the eight columns of slots are then connected to eightRF processing channels 1802. Each RF processing channel comprises atransmit-receive duplexing filter 1803, a linear transmit poweramplifier 1804, an RF amplifier 1805, a downconvertor, IF filter,amplifier and A/D convertor 1806 for each frequency channel, and acorresponding transmit modulator 1807 for each frequency channel, theoutputs of which are summed in summer 1808 before being amplified inpower amplifiers 1804.

The digitized outputs for all eight columns of slots for each frequencychannel are fed to a receive matrix processor 1809. The receive matrixprocessor 1809 is analogous to the matrix processor 650 of FIG. 9. Thematrix processor 1809 separates signals arriving on the same frequencybut from different angles such that cochannel interference from mobilesin communication with the same site is substantially suppressed. Theseparated signals are fed to voice or random access channel processors(not shown in FIG. 18) analogous to channel processors 660 of FIG. 9.Correlation measurements performed by the channel processors (not shown)are fed to a control processor (not shown) analogous to controlprocessor 1702 in FIG. 17. The control processor (not shown) producesboth receive and transmit matrix coefficients for receive matrixprocessor 1809 and transmit matrix processor 1810 to produce atransmitted signal to every cochannel mobile in a non-interferingmanner.

A difference in propagation conditions can arise in landmobileapplications as compared to satellite applications, resulting in somemodifications to the matrix processing that will now be described.Satellite propagation paths are substantially line of sight, and even ifsignal echoes from objects in the vicinity of the mobile occur, thesightlines from these objects to the satellite are substantially thesame as the direct ray from the mobile to the satellite when comparedwith the relatively large cell diameters in satellite-cellular systems.

This is not true for landmobile systems. A substantial echo from a largebuilding or mountain range on the other side of the antenna compared tothe mobile can result in an echo that comes in from a direction anywherebetween 0 and 180 degrees away from the direct ray. Since such echoescarry signal energy, it is often desirable to exploit them to provide adiversity path in the event that the direct ray fades or is shadowed inorder to improve reception. Typically, the signal path from the mobileto the base station antenna consists of a number of rays caused byreflections from objects close to the mobile; these rays are receivedsubstantially from the same direction and combine to produce so-calledRayleigh fading. Since the base station antenna in, for example,large-cell applications is deliberately placed high at a good vantagepoint, there are not expected to be large reflecting objects in closeproximity, for example within 1.5 Km, that could result in rays comingfrom substantially different directions. This means that rays reflectedfrom such objects and coming from an arbitrary direction would beexpected to have traversed a larger distance, e.g., 3 Km, and thussuffered a delay of 10 μS or more.

To take care of both types of the aforementioned phenomena, that is acluster of rays from substantially the same direction causing the signalto exhibit Rayleigh fading as well as a cluster of rays from asubstantially uncorrelated direction representing a delayed signal,another term can be introduced into the receive matrix processing asfollows.

A signal sample Si(t) received at the ith antenna element (column ofslots) is the sum of non-relatively-delayed transmitted signals Tk(t)from mobiles k and signals relatively delayed by dt given by:

    Si(t)=Ci1.T1(t)+Ci2.T2(t) . . . +Cin.Tn(t)+Ci1'.T1(t-dt)+Ci2'.T2(t-dt) . . . +Cin'.Tn(t-dt)

When the equations for all Si(t) are collected into matrix form, theycan be written:

    Sj=C.Tj+C'.T(j-m)

Wherein the suffix j of T means values at a current time and the suffixj-m means values m samples ago, corresponding to the delay dt. Forexample, if the signals are sampled every 5 μS, then for a delay dt=10μS, m would be equal to 2.

The signal fading of the undelayed ray can be considered to be due tovarying C coefficients, with the transmitted signals T being constant,or the signals T can be considered to be varying due to Rayleigh fadingand the matrix C to be constant. The latter is considered here, becauseafter separating the fading signals T by using constant matrices, thevoice channel processors can handle the fading signals as they do inlandmobile systems.

If the signals T are considered to be fading, however, note that thefading on the delayed term is not correlated. In order to be able toconsider Tj-m) as a delayed replica of the fading signals Tj therefore,the difference in fading must be explained by regarding the coefficientsC' as varying to convert the fading on the direct ray to the fading onthe delayed ray. However, infinite values of C' would then arise due tothe varied coefficients being the ratios of Rayleigh fading values.

It is thus more convenient to regard the C-matrices as constant relativeto directions of arrival, and to introduce an explicit set of Rayleighfading variables to explain the fast fading. Each signal in the vectorTj, the first signal t1(j) for example, thus has an associated complexmultiplying factor r1(j) representing the undelayed Rayleigh fading pathfrom mobile 1 to the array. Assembling the factors r1,r2,r3 . . . rndown the diagonal of a matrix, with zeros elsewhere and denoting thisfading matrix by R0, the set of faded signals are then simply given by:

    R0.Tj

Defining a different fading matrix R1 for the first delayed path, thedelayed faded signals are given by:

    R1.T(j-m)

Thus the signals out of the array elements are given by:

    Sj=C.R0.Tj+C'.R1.T(j-m)

According to one aspect of the present invention, separation of thefading signals R0.Tj takes place using the separated signals R0.T(j-m)calculated m samples ago, based on the equation: ##EQU9##

It is seen that the previously separated signals R0.T(j-m) must firsthave their fading factors removed by division by R0 to replace thefading factors for the direct rays with the fading factors R1 for thedelayed rays. This can cause numerical difficulties when a signal fadesout completely so that its associated r-factor becomes zero. However,since the separated signal would also become zero, it is possible toassign a meaningful value to R0.T(j-m)/R0, using, for example, knowledgeof the nature of the transmitted signal. For example, knowledge that thetransmitted signal is a constant amplitude signal, or that it should becontinuous between samples, could be used.

Alternate implementations and modifications of the principles set forthherein will be readily appreciated by those skilled in the art. Forexample, although the signal transmitted in any future cellular systemwill most likely be a digital signal, the principles of the presentinvention are also applicable to analog signals. In both cases, thefading spectra (i.e., the Fourier transform of a successive series ofr-values) are narrowband compared to the modulation, which is the meansby which information in the modulation can be distinguished frommodulation caused by fading. In the case of digital signals, themodulators used at the transmitters are well characterized a-priori, sothat the waveforms Tj that they will produce for a given information bitpattern can be predicted. If a known bit pattern is contained in asegment of transmission, a corresponding segment of the Tj waveforms canbe predicted and correlating this with the received signals will yieldan estimate of the corresponding T-value. This process is referred to as"channel estimation". The channel estimates may be updated afterdecoding each information bit. Due to the channel varying much slowerthan information bits and even more slowly than the sample rate of Tj,which may be, for example, eight times the information symbol rate,channel estimates are averaged over many successive samples of theT-waveforms, and are thus somewhat less noisy than the informationsignals themselves.

In the case of analog FM signals, for example, the modulation is knowna-priori to be constant amplitude, varying only in phase. The rate ofchange of phase is known a-priori to be restricted to a valuecorresponding to the maximum frequency deviation, and the frequencyvariation is continuous and so the phase and at least its first andsecond derivatives are continuous. This a-priori knowledge can be usedto predict a next Tj value from the previous history. For example, ifQ_(ji) was the previous phase estimate and Q its derivative estimate,and A_(j) was the previous amplitude estimate, then T_(j) =A_(j) EXP(_(j),Q_(j)) and T_(j+1) =A_(j) EXP (_(j) (Q_(j) +Qdt)). Hence, T_(j+1)is predicted from T_(j+1) =T_(j) EXP (_(j) Qdt).

Channel estimation techniques often use a Kalman filter includingderivatives, in which a prediction of the next value of the channelestimate is made using an estimate of the time rate of change(derivative) of the signal, then the predicted channel estimate is usedto predict the next signal sample point. The error between the predictedand received signal is then used to correct the estimate of the channel(the fading factor) and its derivative in such a way as to sequentiallyminimize the sum square error.

The same Kalman filter technique can also be used to estimate thediagonal elements of both R0 and R1. Having estimated these diagonalvalues, according to another aspect of the present invention, it isascertained whether any value of R1 is greater than a correspondingvalue of R0. If a value of R1 is greater than a corresponding value ofR0, that would indicate that the delayed ray is currently received at agreater strength than the direct ray. Then the column of C'corresponding to that element of R1 is swapped with the correspondingcolumn of C corresponding to R0 to form new matrices which are denotedby Cmax and Cmin. The greater element from R1 is swapped with thecorresponding smaller element from R0 to form new R-matrices Rmax andRmin, respectively. The elements of T(j-m) corresponding to the swappedR-elements are then swapped with the corresponding elements of Tj toform mixed vectors of delayed and undelayed signals denoted by Uj andVj, respectively. The vector Uj can contain some elements of Tj and someelements of T(j-m), while the vector Vj then contains the remainder.Thus, the equation for signals out of the array elements becomes:

    Sj=Cmax.Rmax.Uj+Cmin.Rmin.Vj

This equation can then be solved to yield:

    Uj= Cmax.Rmax!.sup.-1.  Sj-Cmin.Rmin. Vj!

Since each element of Rmax was chosen to be the greater of two, thechances of zero values are reduced. Furthermore, the Vj values that haveto be subtracted from Sj are minimized by multiplication by Cmin, so ifVj values are wrong or noisy the error propagation into subsequentvalues will be attenuated.

The vector Vj, however, contains some as-yet uncalculated values.Assuming that the same elements of R0 and R1 are chosen for Rmax andRmin next time, the as-yet uncalculated values of Vj belong to a futureU-vector U(j+m). The previously calculated values of T contained in Vjcome from a previous U-vector, U(j-m).

Cmin and Rmin can be partitioned into two matrices Cmin1, Rmin1 andCmin2,Rmin2, the columns of which are associated with the Vj values thatcome from previous or U-vectors, respectively. Thus, the U-vectors canbe described as:

    Uj= Cmax.Rmax!.sup.-.  Sj-Cmin1.Rmin1.U(j-m)-Cmin2.Rmin2.U(j+m)!

The values of U(j-m) are known from a previous calculation, but thevalues of U(j+m) are not. Therefore, Uj is first calculated on theassumption that all U(j+m) are zero. Then, m samples later when U(j+m)has been calculated on the assumption that U(j+2m) are zero, thecalculated values of U(j+m) can be back-substituted into the aboveequation to give a refined set of values for Uj. These Uj values may bethen back-substituted into a previous calculation of U(j-m) to refinethat calculation, and/or forward substituted into the calculation ofU(j+m), or both, to an iterative extent limited only by availableprocessing power in the receive matrix processor.

Simplifying the above equation by denoting:

    Ao= Cmax!.sup.-1

    A1= Cmax!.sup.-1.  Cmin1.Rmin1!

    A2= Cmax!.sup.-1.  Cmin2.Rmin2!

and substituting yields:

    Rmax.Uj=Ao.Sj-A1.U(j-m)-A2.U(j+m)

If A1 has diagonal elements D1 and A2 has diagonal elements D2, then wecan also write:

    D1.U(j-m)+Rmax.Uj+D2.U(j+m)=Ao.Sj-(A1-D1).U(j-m)-(A2-D2).U(j+m)

The left hand side of the foregoing equation represents separatedsignals without cancellation of delayed or advanced rays. The separatechannel processors can process these signals including delayed echoes toobtain better quality demodulation and decoding than if echoes had beensubtracted. The improved decoded signals are useful in better producingthe required channel estimates. A device that can, for example, be usedfor this purpose is a Viterbi equalizer such as described in commonlyassigned U.S. patent application Ser. No. 07/965,848, filed on Oct. 22,1992 and entitled "Bidirectional Demodulation Method and Apparatus",which is hereby incorporated by reference.

Thus, according to this exemplary embodiment of the invention, echoes ofeach signal are subtracted from estimates of other signals, but not fromthe estimate of the signal itself, to produce separation of signal+echosignals that are processed by individual channel processors. Echoes ofeach signal itself are left in additive combination with the signal andare used by a Viterbi equalizer. If echoes are not delayed or advancedby multiples of the modulation symbol period, a so-calledfractional-spaced Viterbi equalizer can be used. Such equalizerscontinuously estimate and update the amount and phase of additiveechoes, as described in commonly assigned U.S. Pat. No. 5,164,961 toBjorn Gudmundson entitled "A Method and Apparatus for Adapting a ViterbiAlgorithm to a Channel Having Varying Transmission Properties", U.S.Pat. No. 5,204,878 to L. Larsson entitled "Method of Effecting ChannelEstimation For a Fading Channel When Transmitting Symbol Sequences", andU.S. patent application Ser. No. 07/942,270, filed on Sep. 9, 1992 andentitled "A Method of Forming a Channel Estimate for a Time VaryingRadio Channel", each of which are incorporated here by reference. Theestimated values correspond to the diagonal elements of the diagonalmatrices D1, Rmax, D2. Knowing Cmax and Cmin, Rmin1 and Rmin2 can thenbe determined, thus the channel adaptive equalizers in the individualchannel processors can determine the Rayleigh fading functions R0 andR1.

A purpose for cancelling by subtraction cross-echoes, i.e., echoes ofone signal that are additive to a different signal, is to provideseparate signal sample streams that each depend only on one signal andits own echoes, as such can be handled by said channel-adaptive, Viterbiequalizers. For completeness however, a further method will now beexplained, that can be used when the number of signals to be separatedis relatively few, for example, eight signals.

The receive matrix processor can be regarded as undoing the additivesignal mixing that takes place in the aether. This is advantageous insimplifying the operation of the channel processors. However, asdisclosed above, numerical difficulties can arise in dealing withsignals that can periodically fade completely. This can result incertain matrices becoming singular, i.e., difficult to invertaccurately. An equivalent problem arises in equalizers that attempt toundo the effect of a corruptive channel, for example a channel thatsuffers from selective fading that causes a null in the transmissionfunction at some frequency. An inverse channel filter that attempts toundo the effect of such a channel would try to create infiniteamplification at the null frequency, with consequent huge amplificationof noise and other difficulties.

Therefore it is often proposed, as in the Viterbi equalizers cited, thatthe channel should not be "undone" by subjecting the received signal toan inverse channel filter to produce an undistorted signal that is thencompared to the alphabet of expected symbols, but rather the alphabet ofexpected symbols is subjected to the same channel distortion as thesignal by use of a mathematical model of the channel, and the distortedreceived signal compared with this predistorted alphabet.

According to a further exemplary embodiment of the present invention, amethod is disclosed whereby no attempt is made to separate or "unmix" inthe receive matrix processor the plurality of co-channel signalsreceived by the array to produce separated signals that are thencompared in separate channel processors with the alphabets of expectedsymbols. Instead, the alphabets of expected symbols are premixed inevery possible way with the aid of a model of the mixing process thattakes place in the aether, (i.e., with the aid of the C-matrixcoefficients and the channel estimates R) and the mixed alphabet is thencompared to the mixed signals received by the array elements.

Such a scheme expands the number of possible mixed symbols in thealphabet exponentially according to a power of the number of signals.For example, suppose each signal is modulated with binary symbols. Theexpected symbol alphabet has only two symbols, 0 or 1. However, if thearray elements receive weighted sums of eight signals, each of whichinstantaneously may be modulated with a 1 or a 0, the number of possiblemixed signals that can be received is 2⁸ or 256, if all the signals arealigned in time. If different signals are not time aligned, then asymbol period of one signal may overlap two symbols of another signal.Thus the waveform over a symbol period of one signal can depend on twosymbols of each of the other signals. Nevertheless, each point of thewaveform depends only on the one symbol of each signal whose symbolperiod it lies in. When echoes are taken into account, however, eachwaveform point can be dependent on two symbols of each signal therebyraising the number of possible values that can be observed to 65536. Itwill however be described below how, for example, a 256-state Viterbialgorithm can be used to jointly demodulate the signals from the array.

According to an exemplary embodiment aspect of the invention, andreferring to FIG. 19, a numerical machine has 256 sets of memory banks1900 each associated with a specific 8-bit postulate for one previousbinary bit in each of the eight signals, on which, due to a delayedecho, the received array signals will depend. The SMLSE controller 1910now makes another 8-bit postulate 1920 for the current binary bit ofeach signal. How it makes this postulate is immaterial, as allpostulates will eventually be tried. In the event that postulates aretried sequentially, they can, for example, be generated by an 8-bitcounter. If however all postulates are tried in parallel usingreplicated hardware, each hardware unit would handle one fixed postulatethat could then just be hard-wired in.

Together which each of the previous 8-bit postulates in turn plus thenew 8-bit postulate, a set of eight signal predictors 1930 predicts thecomplex value of each signal incident on the array including one or morereflected rays by using the fading channel coefficients R and R' anda-priori knowledge of the transmitted modulation or coding. The complexsignal values are then combined in matrix processor 1940 by calculatingthe equation:

    Sj=C.R.Tj+C'.R'.T(j-m)

where C and C' are square matrices representing the directions fromwhich the direct and delayed waves are principally received.

The calculated signals Sj are the signals that are expected to bereceived at the array elements if the hypothetical eight bits arecorrect. These hypothetical signals are then compared with thecorresponding received signals R1,R2 . . . R8 from the array elementsusing comparator 1950. Comparator 1950 evaluates the net mismatch of theeight predictions from the eight array signals by, for example,computing a sum of squares of the differences. Other means to produce asignal representative of the net mismatch are however known to the art,based on a mathematical expansion of the sum of squares, and can be usedif considered advantageous for the particular implementation chosen. Forexample, note G. Ungerboeck, "Adaptive Maximum Likelihood Receiver ForCarrier Modulated Data Transmission Systems", IEEE Trans. Commun. Vol.COM-22 No. 4, pp. 624-636, May 1974, U.S. Pat. No. 5,031,193 to Atkinsonet al., and U.S. Pat. No. 5,191,548 to Backstrom et al., each of whichis incorporated here by reference. The sum square error signal is fedback to the SMLSE controller 1910 which adds the error to the previouserror stored in state memory 1900 against the previous 8-bit signalhypothesis 1921 employed in signal predictors 1930 to produce thesignals ri'ti'.

The above procedure is carried out for each new 8-bit hypothesis in turnpreceded by each of the stored, previous hypotheses. This results, foreach new hypothesis, in 256 candidate cumulative error numbers dependingon which preceding hypothesis was used. The lowest of these is selectedto become the new cumulative error associated with the statecorresponding to the new 8-bit hypothesis. When all possibilities forthe new 8-bit hypothesis have been processed in this way, the statememory 1900 will contain 256 new cumulative error numbers associatedwith each new hypothesis, as well as a record of the best precedinghypothesis to each, i.e., that giving the lowest error, and thepreceding hypotheses to those in turn, and so on. Thus each of the 256states contains a candidate demodulated sequence of 8-bit values. Theoldest values in these sequences will tend to agree and when thishappens the machine is said to have converged to an unambiguousdecision. The decided 8-bits are then extracted to yield one bitdecision for each of the eight incident signals. If convergence does notoccur and the sequence memory 1900 becomes full, the path history istruncated by believing the oldest byte of the state having the lowestcumulative error. That value is then extracted and the path historymemories shortened by one byte.

The above process represents an alternative to attempting to separatesignals that have been mixed by means of matrix processing. Instead,signals are hypothesized by models of the transmitters and models of themixing process, and the hypothesis best corresponding to the observed,mixed signals is determined by the SMLSE machine 1910 in the mannerdescribed above. Thus, the need to invert a mixing process to separatemixed signals, which may be mathematically intractable, is avoided byinstead applying the mathematically tractable mixing process to thehypothesized signals to predict the mixed signals that should bereceived by the array elements and picking the hypothesis that bestmatches the observed signals. This process will not fail when twomobiles using the same channel lie at the same bearing, the process thenbeing equivalent to joint-demodulation as, for example, disclosed inU.S. Pat. No. 5,506,861 granted Apr. 9, 1996 and entitled "A Method andApparatus for Joint Demodulation of CDMA signals with Multipath TimeDispersion".

The above-described exemplary embodiments of the present invention areapplicable to satellite cellular communications systems to providegreater use of available bandwidth by permitting immediate spectrumre-use in adjacent cells. These techniques have also been described inrelation to land cellular systems, where they permit, for example,re-use of the same frequency in adjacent sectors.

In practice, Inn both the satellite and land-based applications of thepresent invention, benefits are achieved by a combination of adaptivesignal processing techniques linked to traffic management techniques.The traffic management techniques relate to continuously operationalsystems using TDMA or FDMA or a combination thereof in which calls arecontinually being terminated and new calls established. By selectivelyestablishing new calls on time- or frequency-slots in such a way as tooptimize a communications criterion, a natural sorting of traffic intogroups using the same timeslot and/or frequency is established. Thecriterion relates to the ease with which the adaptive signal processingcan separate signals on the same frequency and/or timeslot based on thereception of different, linearly independent combinations of them usinga plurality of antenna elements.

According to yet another exemplary embodiment of the present invention,the signal processing does not adapt to the movement of mobile phones orto new call set-up and termination, but operates in a deterministic wayand instead the traffic is adapted to the deterministic characteristicsof the signal processing using a dynamic traffic channel assignmentalgorithm.

Conventional land-based cellular systems typically employ so-calledsectorization, in which a single antenna mast carries three, 120-degreecoverage antennas and illuminates three cells from a common site. Thissaves on real estate costs compared to illuminating the three cellsusing three separate antenna sites at the cell centers. Six sectorsystems are also known. Cellular systems have conventionally employedanalog FM voice transmission in which each conversation is assigned aseparate pair of up-and down-link frequency channels respectively. TDMAsystems are now being installed using digital speech transmission, inwhich each conversation is allocated a unique pair of timeslot-frequencychannel combinations. In these conventional systems, however, the three,120-degree sector antennas have the same radiation patterns for allfrequencies and/or timeslots.

According to yet another exemplary embodiment of the present invention,rotationally offset radiation is provided between different frequenciesand/or timeslots. For example, on frequency channel 1 the three, 120degree sectors may be orientated towards 0 degrees (Due North), +120degrees (South East) and +240 degrees (South West). On frequency channel2, the three sectors may be orientated to 60 degrees (North East), 180degrees (Due South) and 300 degrees (North West). In general one mighthave as many as 120 frequency channels with corresponding antenna sectorpatterns offset by only one degree from each other. Such a system cannotbe implemented using today's fixed-beam cellular base station antennas,but can be arranged with using the exemplary cylindrically symmetricarray and associated matrix processing of FIG. 18.

Similarly, the antenna sector patterns can be rotationally staggered asbetween different timeslots in a TDMA system. In either the FDMA or TDMAor hybrid cases, this exemplary system determines at call set up, andoptionally at regular intervals thereafter, the optimum time- and orfrequency slot combination to use for communicating with the mobilestation. The combination of a frequency and timeslot is abbreviatedhenceforth to simply "channel". The optimum channel is most likely onewhich has an associated antenna sector pattern pointing in the directionof that mobile. This channel would be selected if the selectioncriterion is, for example, maximum signal strength and the channel wasfree. If the criterion is maximum signal-to-interference ratio,different selections can result. Adaptive channel selection methods canbe used to implement the present invention as, for example, disclosed inU.S. Pat. No. 5,230,082 to Ghisler et al. which is incorporated here byreference.

FIG. 20 illustrates a set of staggered sector patterns that can beproduced by the arrangement of FIG. 18 using fixed matrix coefficientsfor each frequency channel of an FDMA system. Three lobes are created inthis example on every frequency channel. The notation Pi(Fk) indicatesthe pattern of the i^(th) lobe on the k^(th) frequency channel. Thematrix processing coefficients are preferably chosen such that P1(Fk)and P2(Fk) have minima where P3(Fk) has its maximum, and reciprocally.If the minima are zero, the three lobes are said to be orthogonal. Thatpermits a mobile located in the nulls of P1 and P2 to receive maximumsignal from P3 with no interference from the other two, which can thuscarry separate signals. In general, true zeros will not be perfectlyachieved, and the channel selection criterion will thus allocate amobile to a frequency where the corresponding sector patterns result inmaximum ratio of wanted signal to unwanted interference from other lobesand other cells. For example, the mobile M in FIG. 20 would be allocatedpreferably F4, where the lobe P3(F4) has the maximum strength in thedirection of the mobile M. If P3(F4) was not available, the next bestallocation P3(F3) would be tried, and so on.

In practice, an FDMA cellular system such as AMPS has 1000 channelsavailable, usually divided between two operators that handle a minimumof 400 each. Using the traditional frequency re-use pattern of 21, thisresults in around 20 frequencies being available in every cell or 60 persite. The angular difference between lobes on different frequencieswould thus, in a three lobe system, be only 1/20th of 120 degrees or 6degrees. In this example, different lobes at the same site all havedifferent frequencies. Assuming uniform distribution of mobiles inangle, the channel allocation algorithm would result in each mobilebeing within a few degrees of beam center. This results in mobilesreceiving better signals on average than in today's fixed sectorizationpatterns which, when optimized, are around 12 dB down at sector edges.If the wanted signal is improved in this way, the tolerance ofinterference from surrounding cells is improved such that the re-usepattern can be shrunk from 21 to a tighter re-use pattern such as 12,with a consequent capacity gain of 21/12. This can be achieved using thesame number of lobes as sectors in today's cellular systems. If thenumber of lobes is increased to eight, as illustrated in FIG. 18, afurther 8/3 increase in capacity is obtained, to around five timescurrent AMPS capacity. Moreover, allowing every cell to adoptivelyselect any of the 400 frequency channels in attempting to maximizesignal to interference ratio gains a factor of two in capacity relativeto having a fixed subset of frequencies (1/21st or 1/12th of the total)in each cell. This is achieved when transmit power levels are alsoadapted to the varying radial distance of each mobile from its cellsite. It is also possible to use all 60 site frequencies in each 120degree sector by making lobes using the same frequency orthogonal, asdefined above. Lobe separation is then 2 degrees and the channelallocation algorithm ensures not only that each mobile is within acouple of degrees of beam center, but also within a couple of degrees ofthe minima of the co-frequency lobes.

If instead of associating staggered sector radiation patterns withdifferent frequency channels F1,F2,F3 . . . they are associated withdifferent timeslots of a TDMA signal using a single frequency, theresulting radiation from the base station antenna will take a certainset of directions for timeslot 1, a set of rotated directions fortimeslot 2 and so forth, such that the beams are apparently rotatingwith time. Thus in the TDMA context this exemplary embodiment of thepresent invention may be formulated in terms of creating beams whichcontinuously rotate through 360 degrees over a TDMA frame, or moreappropriately, rotate by 360/N degrees during a TDMA frame where N isthe number of sectors of frequency re-use, and the data modulation forthe next frame is shifted back one sector between successive frames suchthat data for the same mobile continues to be radiated in the samedirection. Data destined for a particular mobile is indicated in the USIS54 TDMA system by inclusion of a "Digital Voice Color Code" (DVCC) inTDMA bursts. Thus, for example, this technique can be described moresimply in terms of rotating the antenna sector patterns in one directionwhile rotating the DVCC in the reverse direction at the same rate suchthat the same DVCC continues to be radiated in the same direction onsuccessive frames.

Both exemplary FDMA and TDMA embodiments of the present inventionprovide mobile stations with the capability to determine coarsegeographic position. In the FDMA version, the mobile measures relativesignal strength on different frequencies. The frequency on which thegreatest signal strength is received indicates the bearing of the mobilewithin a sector. The sector is determined by decoding sector IDinformation contained within the transmission.

In exemplary TDMA embodiments, the mobile does not even have to changefrequency. The mobile instead notes the cyclic signal strength variationduring a TDMA frame and then determines the peak and trough signalstrength positions relative to timeslot 1, which can be identified bythe slot ID information carried in each slot.

The cyclic signal strength variation can be processed over severalcycles with the aid of a Fourier transform and the phase of thefundamental component relative to timeslot 1 will then indicate themobile's bearing. Bearings from two base stations of known positionsthen fix the mobile position. The mobile can report the timing of signalstrength peaks and the network can perform the position calculation,rather than the network having to send coordinates of base stations tothe mobiles. Upon allocating a traffic channel to a called or callingmobile, the network can then determine the best of all availabletimeslot/frequency combinations to use.

The above-described can also be adapted to provide advantageouscommunications between mobile stations and an orbiting satellite.According to this embodiment, the antenna array signal processing is notadapted to various mobile positions, but rather mobiles are allocated toa specific antenna array signal processing channel based on position insuch a way as to optimize communications. That is, mobiles areadaptively allocated to communicate using one of a number of fixed,staggered antenna beam positions instead of adaptively steering theantenna beams onto the mobile positions.

The operation for satellite use may be modified slightly. The notion offixed antenna beams would be applicable to a geostationary satellite,but may not be applicable to, for example, a low-orbit satellite thatchanges position relative to the earth. Then the position of a beamrelative to a given mobile would move due to satellite motion if not dueto mobile movement. If the satellite beams move over the earthrelatively slowly in comparison with the average 3-minute call duration,it may be sufficient to allocate a mobile lo a beam at call set up, asone would in the Geostationary case. However, according to thisexamplary embodiment of the present invention, beam directions can beadapted to remove the systematic motion of the satellite over the earthso that the area illuminated by each beam is static from satellite riseto satellite set. In this way, a mobile may remain allocated to the samebeam irrespective of satellite movement during this period.

Furthermore, such a system of low-orbiting satellites would generally bearranged to provide continuous coverage whereby as one satellite sets,another rises. For example, it can be arranged that a satellite risingin the west takes over the illumination of the same area just beingvacated by a satellite setting in the east. Then, as the adjacent areato the east of this experiences loss of the setting satellite, therising satellite creates a new beam to dovetail in while havingmaintained the first beam over the original area, and so on until thenew satellite has taken over illumination of all areas originally servedby the setting satellite.

Thus, the application of this exemplary embodiment of the presentinvention in the case of moving satellites allows the illuminationpatterns from the satellite antenna to be compensated for satellitemotion so as to illuminate fixed areas of the earth while adaptivelyallocating mobiles to illumination patterns using a channel assignmentalgorithm that optimizes a communications quality criterion. Thiscontrasts with mechanical methods of compensating for satellite motionby tilting the satellite or antenna so as to maintain the center pointof at least one area constant. This mechanical method, however, cannotmaintain the center points of cell illumination areas constant due tothese areas changing shape from circular as the satellite moves overheadto elliptic and finally to parabolic at earth-edge illumination.Alternatively, this exemplary embodiment of the present invention canemploy both a mechanical method for coarse compensation plus the methodof adaptive antenna array signal processing to correct the illuminationpatterns for shape change as the satellite moves. Alternatively, signalprocessing can be used to hold the areas served by a particularfrequency and/or timeslot constant while progressively creating newareas forward of the satellite's ground track that are being vacated bya setting satellite and while terminating illumination of areas to therear of its ground track that are being taken over by a risingsatellite.

The operation of this exemplary embodiment of the present invention isdepicted in FIGS. 21(a) and 21(b). At a certain time T (FIG. 21(a)) arising satellite 2100 illuminates areas with frequencies (left to right)F1,F2,F3,F1,F2,F3,F1,F2 and a falling satellite 2102 illuminates furtherareas with frequencies (left to right) F3,F1,F2,F3,F1,F2,F3,F1 whichcontinue the frequency re-use sequence. At, for example, time T+5minutes (FIG. 21(b)) the rising satellite 2100 has ceased to illuminatethe rearmost F1 area 2104 which is presumably now obscured from view(i.e., the satellite is too low on the horizon for good communicationswith this area) while the setting satellite 2102 has stoppedilluminating its rearmost area 2106 with frequency F3 for the samereason.

On the other hand, the rising satellite has created a new illuminationarea 2107 forward of its ground track to fill in the area vacated by thesetting satellite. The rising satellite 2100 can appropriatelyilluminate the new illumination area 2107 with the same frequency as itspredecessor used. Meanwhile, the satellite 2102 that is setting withrespect to this area is rising as viewed from areas ahead of its groundtrack, and uses the released capacity to create a new area 2108 forwardof its ground track illuminated with frequency F2.

It will be appreciated that instead of different frequencies, theoverlapping areas could have been allocated different timeslots in aTDMA frame, or different frequency/timeslot combinations in a hybridFDMA/TDMA system. Either way, the availability of a large number ofchannels allows the overlapping beams to be much more finely spaced thanin the example of FIGS. 21(a) and 21(b), so that it is almost equallyeffective to allocate a mobile to an adjacent beam as to the optimumbeam. Logically, one should allocate a mobile preferably to a beam inwhich the mobile is centrally located. However if the correspondingchannel is occupied, the mobile can be allocated to a slightlyoff-center beam and may be handed over to the on-center beam when thecall using that channel terminates.

In the exemplary TDMA embodiment, the rising satellite and the settingsatellite can both illuminate the same area using the same frequency,providing different timeslots are used. Thus, a channel and satelliteallocation strategy according to the present invention is to allow callsin the changeover region to terminate naturally on the setting satelliteand to re-employ their vacated timeslots in the same region and on thesame frequency to set up new calls using the rising satellite.

FIG. 22 is a block diagram of an exemplary control processor thatsupplies the matrix coefficients to the numerical matrix processor ofthe hub station, e.g., block 1603 in FIG. 13. Inputs to the controlprocessor 2200 include satellite orbital data including attitude controlinformation from the independent satellite Telemetry, Tracking andCommand (TT&C) subsystem (not shown). Using satellite orbital andsatellite antenna pointing information (attitude control information)and an input from a real time clock, the control processor 2200 candetermine the matrix coefficients needed such that a given area will beilluminated by a specific frequency in a specific time slot. Thesecoefficients are systematically updated in step with changes in the realtime clock to maintain these illuminated areas approximately fixedirrespective of satellite motion. The control processor 2200 alsoreceives information transmitted from mobile stations malting a randomaccess on a calling channel that allows the control processor todetermine the best available channel/beam combination to use. Thisinformation provides a rough indication of the location of the mobileand the control processor then determines the available beam centeredmost closely on this location. This in turn determines the frequencyand/or timeslot that should be used for communication with the mobile.

It will be apparent to one skilled in the art that TDMA and FDMA are notthe only access methods that are compatible with the present invention.Code Division Multiple Access (CDMA) can also be used, whereillumination areas are similarly staggered over the earth according to aCDMA code use pattern. Indeed, any multiple access method which definesa channel by means of a set of access parameters can have systematicallystaggered illumination areas depending on those access parameters.Moreover, the access method used on the downlink can be different fromthe access method used on the uplink, providing a set of uplink accessparameters is paired with a corresponding set of downlink parameters ineach offset beam or staggered illuminated area. For example, acombination of TDMA on the downlink with CDMA on the uplink, the uplinktransmission being continuous apart from a short interruption duringreception of the downlink slot, is disclosed in U.S. Pat. No. 5,539,730granted Jul. 23, 1996 and entitled "TDMA/FDMA/CDMA Hybrid Radio AccessMethods", which is incorporated here by reference. Having described anexemplary embodiment wherein dynamic traffic channel assignment allowstraffic to be adapted to the deterministic characteristics of signalprocessing, a complementary, exemplary embodiment will now be describedwherein capacity can be optimized through coding and frequency re-useschemes.

The ultimate capacity of a cellular satellite communications is limitedby available bandwidth, as power limitations can always be solved bymoney, e.g., by launching more satellites. Practically, however, thereare financial constraints on power and political constraints onbandwidth, therefore it is desirable to use bandwidth efficientlywithout significant sacrifice of power efficiency.

It shall be appreciated that the trade-off of bandwidth and powerefficiency for a cellular (i.e., area or global coverage system) isdifferent from that of a single link, as a single link trade-off doesnot consider the possibility of frequency re-use in adjacent cells. Theunits of capacity in the two cases are in fact different, beingErlangs/MHz for a single link and Erlangs/MHz/SqKm for a cellularsystem.

A cellular system illuminates a service area by dividing it into cellsand using some fraction 1/N of the total available bandwidth in each. Acluster of N neighboring cells can thus be allocated different 1/Nfractions so that they do not interfere. Outside the cluster, for cellsfar enough away, the bandwidth can be re-allocated to another cluster.

The reduction of interference by employing an N-cell re-use pattern ismeasured in terms of the carrier to interference ratio C/I, which is theratio of wanted signal power to the sum of the power of all unwantedspectrally and temporally overlapping signals. Increasing N increasesthe C/I, but reduces the bandwidth available in every cell, therebylimiting system capacity. Reducing N worsens C/I but increases thebandwidth available to every cell. If the modulation and coding schemecan tolerate the reduced C/I, capacity will thus be increased byreducing N.

One method of providing greater C/I tolerance is to use redundantcoding. This method increases the bandwidth per signal, however, whichoffsets the benefit conferred by shrinking the re-use pattern N. Thequestion to be asked is where the optimum lies.

In land-based cellular systems, this question has been deeply studied,leading some people to conclude that the extreme bandwidth expansion ofCDMA techniques combined with immediate frequency re-use in every cellprovides the highest capacity. According to exemplary embodiments of thepresent invention, however, it is found that capacity increases withincreasing coding and reduction of N until N=1 is reached with a codingrate of about 1/3 (for landcellular). At this point the system is notregarded as being truly CDMA as each channel is still only used once inevery cell. CDMA can be defined as the use of each channel more thanonce in each cell, i.e., a fractional value of N. For example, N=1/2means each channel is used twice in every cell, which would beclassified as CDMA.

Whether this further reduction of N to fractional values continues toincrease capacity depends on what type of CDMA system is employed and onthe nature of the propagation channel and receiver complexity used inthe system.

Three types of CDMA systems may be distinguished:

i) Conventional, non-orthogonal CDMA

ii) Orthogonal CDMA

iii) Interference cancellation CDMA (subtractive CDMA, jointdemodulation, etc.)

For the landbased cellular world, it is found that the capacity dropsoff below N=1 for CDMA of type (i), levels off for orthogonal CDMA(which is really equivalent to giving every signal a unique frequency ortimeslot) and increases for systems of type (iii). Moreover, the gainfound in systems of type (iii) for landbased cellular where N<1 is dueto the high near-far environment such that the interference averaginginherent in CDMA techniques includes many transmitters of significantlyreduced power, and due to the landbased cellular scenario being C/Ilimited rather than noise, C/No, limited. Neither of these features arerelevant to satellite communications systems. Accordingly, the presentinvention explores what kind of coding/frequency re-use trade-off wouldmaximize capacity for a given bandwidth allocation in C/No-limitedsatellite communication systems.

The signal spillover between cells in a landbased cellular system is afunction of the fourth-power-of-distance propagation law. Incellular-satellite systems C/I is a function of antenna beam patternsidelobes. It is necessary therefore to develop some model of antennabeam patterns to perform coding optimization.

The beam pattern of the antenna depends on the surface currentdistribution over the aperture, called the aperture illuminationfunction. Without invoking the supergain phenomenon, the most efficientuse of aperture is obtained with uniform illumination. This gives thebest gain but the highest sidelobes. The radiation pattern is plotted inFIG. 23 for a uniformly illuminated circular aperture. The sidelobes inthe E and H planes are slightly different owing to an extra cosinefactor that appears in the plane containing the surface current vector.This difference manifests itself as cross-polarization components whencircular polarization is employed. Henceforth the E and H plane patternswill simply be averaged for the calculation of C/I.

Reference is made again to FIG. 5 which illustrates a 3-cell frequencyre-use pattern, wherein the shaded cells use the same channel f1 whilethe others use f2 or f3. This re-use pattern will be used to investigatethe coding/frequency re-use tradeoff for satellite communications,however, those skilled in the art will appreciate that any re-usepattern, e.g., 7, 9, 12, 21, etc., could be used. Interfering cells lieon the points of a hexagon and it suffices to consider the first tworings of six interferers. Before their interference levels can becomputed however, it is necessary to choose the correct scaling of thebeam pattern to match the cell diameter.

If the beams are scaled to cross at -3 dB relative to peak gain midwaybetween two cells, it is well known that this does not result in maximumbeam-edge gain. A higher gain is achieved if the beam is narrowed, whichincreases the peak gain more than increased edge-loss experienced.

FIG. 24 is a plot of peak gain 2401 (at the center of a cell), edge gain2402 (midway between two cells) and the gain midway between three cells2403 as a function of the two-cell crossover point in dB down from peak,relative to the peak gain of the -3 dB crossover case. For reasons thatwill be explained later, the two-cell edge gain has been scaled by afactor of two in this plot (i.e., 3.01 dB is added) and the 3-cell edgegain has been scaled by a factor of 3 (i.e., 4.771 dB has been added).This does not affect where the respective gains peak, but affects theperception of which of the three is the worst case. According to thisgraph, the worst case occurs midway between two cells, and the worstcase gain is maximized when the 2-cell edge is 3.8 dB down on the peakgain, i.e., at point 2404.

The way in which the C/I parameter depends on the beam crossover pointis shown for the 3-cell re-use pattern of FIG. 5 in FIG. 25. FIG. 25 isplotted as a function of mobile station distance from beam center forcrossover points of -3, -3.5 and -4 dB showing that C/I over most of thecell radius increases if the beams are narrowed beyond that which givesmaximum edge gain. If necessary, choosing a crossover point of -4.5 dBwould cause negligible loss of edge gain while improving C/I at cellcenter by a further 3 dB to about 20 dB. C/I at cell edge according toFIG. 4 would be just less than 10 dB, but this includes the unmitigatedbeam edge crossover loss which, as will be explained later, will not beincurred because no mobiles need be located there.

If mobiles assigned to a particular channel and beam are chosen to bethose located within 25% of the maximum cell radius, the C/I for allpoints within that area will be as plotted in FIG. 26. The worst caseC/I is maximized to about 23 dB with a beam crossover design point of-5.5 dB, somewhat beyond that which gives maximum edge gain, so inpractice the -4.5 dB crossover point would be used, giving a worst caseC/I of 18 dB.

The same calculations are now repeated for the N=1 frequency re-usepattern, i.e., immediate frequency re-use in adjacent cells, and resultsare plotted in FIG. 27. This shows a cell-center C/I of 14 dB for the -4dB crossover case, but a cell edge C/I of about -1.5 dB. The thicknessof the curves in FIG. 27 is due to superimposition of plots for allmobile angular positions in the cell, and dependence on angular positionis a little more noticeable in the N=1 case than the N=3 case. The first6 rings of 6 interferers were summed to obtain the plot of FIG. 27.

Again, as will be shown later, mobiles using a particular channel andbeam can be restricted to those lying within 25% of beam center or less,so it is of interest to maximize the worst case C/I within this region,as shown in FIG. 28. The worst case C/I in this case maximizes at 13 dBby choosing the beam crossover point to be -4.8 dB, but this may berestricted to -4.5 dB to avoid loss of beam edge gain for only a smallreduction in C/I to 12.5 dB.

FIGS. 29-34 give the results for repeating the whole process describedabove for a different aperture illumination function, the 1/2-cosinewave. This aperture illumination function is slightly lessaperture-efficient than a uniform distribution, but gives lower sidelobelevels (see FIG. 29) leading to higher C/I, particularly in the 3-cellre-use case (20 dB over whole cell, or 27 dB out to 25% of radius). Asseen in FIG. 34, the C/I for immediate frequency re-use out of 25% ofcell radius is 13.5 dB with the practical beam-edge crossover point of-4.5 dB. Since this was 12.5 dB for the uniform illumination, case ofFIG. 28 it should be noted that this value is not very sensitive to theaperture function being used.

The bit error rate is generally plotted as a function of Eb/No, which isequal to the ratio of signal power to the noise power if it were to bemeasured in a bandwidth equal to the bit rate. The latter does not implyany assumption that any physical receiver filter bandwidth must be equalto the bitrate; it is only that "bitrate" is a convenient unit ofbandwidth for defining the noise density with which the performance ofany given receiver will be tested. The receiver error rate performancewill of course depend on the choice of its bandwidth, and that whichoptimizes performance at a given Eb/No may be greater or less than thebitrate depending on the modulation and coding being used.

The C/I parameter is, by contrast, the ratio of wanted to unwantedsignal power in the physical receiver bandwidth. This ratio, however, isindependent of the choice of receive filter if the C and I have the samespectral shape and are thus equally affected by the filter. With thesimplification that any `I` passed through the receive filter will havethe same effect on error rate as an equivalent amount of white noise,NoB, passed by the filter, where B is the noise bandwidth, the effect ofI can be expressed in terms of an equivalent increase in noise densityNo by an amount Io to No+Io, where Io is given by

I=Io.B i.e. Io=I/B

For BPSK modulation, the optimum receiver bandwidth is indeed equal tothe bitrate, while for QPSK modulation the optimum receiver bandwidth isequal to half the bitrate. The bitrate here though is the codedbitrate/chiprate, whereas the bitrate for defining Eb/No is theinformation rate. Thus:

B=Bitrate/r for coding rate r in the BPSK case,

B=Bitrate/2r in the QPSK case, and for general M-ary modulation,

B=Bitrate/rLog₂ (M)=Bitrate/mr where m is the bits per symbol.

Therefore the total bit energy Eb to noise plus interference densityratio is given by: ##EQU10##

For less than 0.5 dB degradation of the Eb/No required for a given errorrate due to finite C/I, the value of mr.I/C should thus be one tenthNo/Eb.

For example, if the ratio Eb/No without interference of 3 dB is desired,then to operate at 3.5 dB Eb/No the C/I must be 10 mr.Eb/No. For BPSK orQPSK and different code rates, the required C/I for exemplary codingrates is given below:

    ______________________________________                                        REQUIRED C/I using BPSK    QPSK                                               ______________________________________                                        Coding rate 1 (none)                                                                             13.5 dB 16.5 dB                                            1/2                10.5 dB 13.5 dB                                            1/3                 8.7 dB 11.7 dB                                            1/4                 7.5 dB 10.5 dB                                            ______________________________________                                    

The above is for a static channel and does not take into account thatlower Eb/Nos are needed with lower rate codes for the same error rate.

"Error Correction Coding for Digital Communications" by Clark and Caingives the required Eb/Nos for 0.1% BER for constraint length 6convolutional code rates of 1,3/4, 2/3, 1/2 and 1/3 as follows:

    ______________________________________                                        r         Eb/No for BER = 0.1%                                                ______________________________________                                        1         6.7 dB                                                              3/4       3.9 dB                                                              2/3       3.5 dB                                                              1/2       3.0 dB                                                              1/3       2.6 dB                                                              ______________________________________                                    

By extrapolation it may be estimated that rate 1/4 would require 2.3 dBwith diminishing returns thereafter. Using these Eb/No figures, the C/Irequired for less than a given degradation are calculated to be:

    ______________________________________                                               REQUIRED C/I                                                                  for 0.5 dB                                                                              1.0 dB loss 3.0 dB loss                                             BPSK  QPSK    BPSK    QPSK  BPSK  QPSK                                 ______________________________________                                        Coding rate 1                                                                          17.2 dB 20.2 dB 13.7  16.7  9.7   12.7                               (none)                                                                        3/4      13.2    16.2    10.9  13.9  6.9   9.9                                2/3      12.2    15.2    8.7   11.7  4.7   7.7                                1/2      10.5    13.5    7.0   10.0  3.0   6.0                                1/3      8.3     11.3    4.8   7.8   0.8   3.8                                1/4      6.8     9.8     3.3   6.3   -0.7  12.3                               1/5      5.7     8.7     2.2   5.2   -1.8  1.2 dB                             ______________________________________                                    

Thus, while the Eb/No for a given error rate levels out with increasingcoding, the C/I required continues to decrease due to the continuallyincreasing bandwidth. This equates to the separate concepts of codinggain (which applies to Eb/No) and processing gain (which applies toC/I). Coding gain is bounded by Shannon's limit, while processing gaincontinues to increase with bandwidth as in a CDMA system.

The above results for the static channel are pessimistic for fadingchannels. When Rician or Rayleigh fading is present, the mean Eb/No canbe increased above the static Eb/No requirement to maintain the sameerror rate. However, on the satellite downlink the C/I does not exhibitfading, because both the I and C reach a given mobile over exactly thesame channel and fade by exactly equal amounts. Thus the C/I does notdecrease by 10 dB when the Eb/No fades 10 dB, but instead stays at theoriginal value.

In the fading channel, since the error rate at the mean Eb/No isconsiderably less than the target value, and when it fades to the staticEb/No value still only equals the target value, it is clear that theerror rate only reaches the target value by virtue of fades to below thestatic Eb/No value. In fact it can be shown that the preponderance oferrors arise from the instantaneous Eb/No region well below the staticEb/No value, where the same C/I causes less degradation. It can beassumed that lower C/I values can be tolerated in conjunction with thehigher Eb/No values needed to account for fading.

Thus the 12.5-13.5 dB C/I values achievable out to 25% of beam radiuswith immediate frequency re-use are acceptable with coding rates of 1/2to 1/3 and using QPSK. Increasing the re-use pattern to N=3 would yield3 times less bandwidth per cell, requiring that all coding be removedand even higher order modulations than QPSK to be contemplated in orderto achieve the same bandwidth efficiency, but with the penalty ofneeding considerably higher power (e.g., Eb/No of 7.7 dB to 10.7 dB forachievable C/I's with the 3-cell re-use pattern). Thus there is no gainin bandwidth efficiency using an N=3 or greater frequency re-use patterninstead of N=1, only a major penalty that either is paid in powerefficiency (for maintaining the same bandwidth efficiency by removingcoding, as in the AMSC system) or in bandwidth efficiency if coding isretained.

To make use of the above result it is explained below how use of a beamcan be restricted to mobiles located, for example, only out to 25% ofthe beam radius or less.

A gain of up to 2:1 in capacity can be achieved in cellular systems witha type of frequency planning known as "re-use partitioning". In a simpleform of re-use partitioning, the available channels in a cell arepartitioned into three sets that are preferentially used for a) mobileswithin the inner 1/3 of the total cell area; b) for mobiles between 1/3and 2/3 of the cell area, and c) for mobiles in the outer 1/3 of thecell area. Assuming a uniform area distribution of mobiles within thecell, this partitioning achieves equal demand for each of the channelsets. The allocation of channels to equal area rings is then permuted inthe neighboring cells according to a 3-cell re-use pattern with theresult that no two neighboring cells use the same channel out to theirmutual border, with consequent increase in C/I for no loss of capacity.The overall re-use pattern to achieve a given C/I may then be shrunk toachieve an increase in capacity. Based on the foregoing principles,re-use partitioning and coding can be optimally combined according toexamplary embodiments of the present invention which will now bedescribed.

FIG. 35 shows a simplified example form for the case where threechannels or groups of channels (which may be frequencies, timeslots,codes or combinations thereof), designated by the colors black, red andgreen are available in every beam. The beam edges at the designcrossover point (e.g., -4.5 dB) are shown by the larger colored circlesof FIG. 35.

The large black touching circles thus refer to beams using the "black"channel and touch at -4.5 dB down from the peak gain. The large redtouching circles represent the beam patterns for the red channel. Theseare displaced relative to the "black" beams, and this fixed displacementis achieved for example by modifying the phases of a phased array forthe "red" channel relative to the "black" channel. It may also beachieved by use of a multiply-fed parabolic reflector, in which theunmodified beam patterns are used for the "black" channels, but in whichthree adjacent feeds are energized each with 1/3rd of the energydestined for a "red" cell. Due to coherent addition, the gain in thecenter of the "red" cell will be 3 times a "black" beam gain at thatpoint, effectively "filling in the hole". The "green" beams are formedin exactly the same way for the "green" frequency or timeslot. This isachieved using ground based hardware that directs the appropriatecombination of signals through the transponder channel directlyassociated with each of the feeds.

In FIG. 35, the smaller circles show the areas out to which a particularchannel is to be used, beyond which a different channel is availablewith a more centrally directed beam. The area has been filled in in thecase of the black beam to assist in identifying it. This area extendsfrom the center of a beam out to the beam radius over root(3), that isthe "cell" area is only 1/3rd of the "beam" area, and mobiles in the"cell" only use the "beam" out to slightly more than 50% of the beamradius.

In practice, of course, many more than three channels are available perbeam, so it is possible to plan for cells that are only 1/M of the beamspot area where M is the number of channels available. If M=7 forexample, beams are only used out to 1/root(7) of their radius, asillustrated in FIG. 36. In practice M will be at least 100, so cellradius can be 1/10th of the beam radius, hence the gain and C/Iperformance of the beam configuration is only important for a fractionof the beam spot coverage. This does not necessarily mean it is possibleto shrink the spot to obtain more gain, as it would not then be possibleso easily to "fill in the holes". With a large number of offset beams itis desirable to phase the physical feeds to produce peak gain anywhere,and as indicated by FIGS. 24 and 30. The hardest place to obtain gain(by phasing only two feeds together) is midway between two spots, andthe gain under those circumstances is maximized by choosing the beamedge crossover points as indicated on FIGS. 24 and 30. The gain betweentwo beams is then twice the beam edge gain (e.g., 3 dB up) while thegain between three beams is three times the gain of one beam at thatpoint. This explains the scaling used on FIGS. 24 and 30 for comparingthe gain at those three points.

Thus, the error correction coding of rate between 1/2 and 1/3 which is,in any case, contemplated for power efficiency reasons, can also providetolerance of the C/Is obtained with immediate frequency re-use in everybeam, if the technique of re-use partitioning just explained above isemployed. The technique of re-use partitioning achieves this withoutresort to null-creation or interference cancellation, i.e., all antennadegrees of freedom are used to maximize gain. The technique ofinterference cancellation or creating pattern nulls at the center ofneighboring cells can be employed as a further bonus to reduce C/I fromneighboring beams to negligible proportions.

An exemplary coding scheme which can be used to implement this exemplaryembodiment of the present invention is punctured convolutional codingbased on rate 1/4 or 1/5th, but in which the coding of each uncodedspeech bit is adapted according to its perceptual significance to alevel between, for example, rate 1/2 and rate 1/5. Although BPSKtolerates 3 dB lower C/I than QPSK, there seems no reason to incur the2:1 bandwidth efficiency loss. The C/I tolerance of QPSK with twice thecoding is in fact better than BPSK with half as much coding, therefore aquaternary modulation can be used at least for the downlink.

The above discussion is based on coherent demodulation performance,which is achievable in the satellite-to-mobile channel using quitewideband TDM and is not achievable with narrowband FDM. The criterionfor the downlink method is that the number of information bits to bedemodulated and decoded shall be large over the time during which thefading component of the channel can be considered static, that is about200 μS at 2.5 GHz and a vehicle speed of 100 Km/Hr. Thus the informationrate needs to be a couple of orders higher than 5 Kb/s and with, forexample, a 1/3 mean coding rate the transmitted bit rate needs to begreater than 1.5 Mb/s, which will pass through a 1 MHz bandwidth channelusing quaternary modulation. The capacity provided by systems based onthe foregoing techniques is of the order of 100 Erlangs per MHz per spotarea using a 4 Kb/s vocoder or 166 Erlangs per MHz per spot using a 2.4Kb/s vocoder.

One exemplary technique for implementing the above-described re-usescheme of the present invention is by means of ground-basedbeam-forming, as described earlier in this specification. This involvesproviding feeder links to carry the signal for each antenna feed fromthe central ground station to the satellite in such a way that therelative phase and amplitude differences between the signals ispreserved. Using such a coherent transponder, only one transponderchannel is needed on the satellite per antenna feed point.

An alternative means of implementing the present invention for thefixed-beam case disclosed is set forth below, which avoids the need forcoherent feeder links at the expense of more hardware on the satellite.The use of on-board beam forming is simplest if it is fixed and notvariable, which may be more suited to a geostationary satellite thatilluminates fixed areas. For a non-geostationary satellite thisexemplary embodiment of the present invention can still be employed, butit is not then so easy to obtain the advantage of systematicallyadapting the beam forming to compensate for satellite motion so thatbeams illuminate fixed areas.

The implementation of the fixed beam-forming transponder is shown inFIG. 37 for the FDMA case, i.e., the total available bandwidth isdivided into N sub-bands, each of which is used to illuminate areas onthe ground according to a cellular re-use pattern such as shown in FIG.35. The case of three sub-bands--designated black, red and green as perFIG. 35--is used by way of illustration.

A set of transponder channels 37 receive signals from a correspondingset of feeder links and downconvert them to a suitable intermediatefrequency for amplification and filtering. The I.F. outputs of 3710 areapplied to I.F. beam-forming network 3720 which forms weightedcombinations of the I.F. signals. The "black" channels are arbitrrilychosen to correspond directly to unmodified antenna patterns, i.e.,black signal 1 shall be radiated directly and only through antenna feednumber 1; black signal 2 shall be radiated only through antenna feednumber 2, etc. The beam-forming network thus connects black channelswith unity weighting into only that summing network corresponding to thedesignated antenna feed.

The red channels and green channels however shall be radiated with abeam pattern centered midway between three black beams. The red beamthat shall lie midway between black beams 1, 2 and 3 is thus connectedto their associated three summing networks through voltage/currentweightings of 1/root(3) (power weightings of 1/3). One third of the"red" energy is thus radiated through each of the three feedssurrounding the desired "red" center. Likewise, the green beam lyingmidway between black beams 2, 3 and 4 is connected via weightings of1/root(3) to the summers associated with feeds 2, 3 and 4. Theweightings quoted above are exemplary and simplified for the purposes ofillustration. Since the I.F. beamforming network can in principle berealized with a network comprising mainly simple resistive elements,more complex sets of weights can be used with acceptable complexityimpact. For example, a beam can be formed by feeding more than threeadjacent feeds, and negative weights can be used to create nulls in theradiation pattern at desired places or otherwise to reduce the sidelobelevels in order to increase the C/I.

One method to form a resistive I.F. beamforming network uses acontinuous sheet or thin film of resistive material deposited on aninsulating substrate. This sheet is notionally regarded as correspondingto the two dimensional surface to be illuminated by the beams. Signalcurrents corresponding to the "black" beam signals are injected into thesheet at points disposed in correspondence to the centers of the "black"cells, while "red" and "green" signal currents are injected at sets ofpoints midway between the black signal injection points and each other,as per FIG. 35. FIG. 38 illustrates the injection points by the labels`I`.

Signal currents corresponding to the desired combinations of the black,red and green signals are extracted from the resistive plane by contactsdisposed midway between the black, red and green injection points. Thesecurrent extraction points are indicated by `E` in FIG. 38. Thistechnique provides the same weight distributions for the black, red andgreen beams, in contrast with the previous example that had singleweights of 1 for the black beams and three equal weights of 1/root(3)for the red and green beams. Extracted currents are fed to "virtualearth" amplifier inputs or low-input impedance amplifiers such asgrounded base bipolar transistors. The set of weights realized by thistechnique can be tailored by choice of the shape and size of the currentinjection and extraction contact lands. No simple rule is proposed fordeciding the size and shape--a proposition must simply be verified bycarrying out a two-dimensional finite-element computer analysis of thecurrent flow in and potentials existing on the resistive sheet.

Once the combined signals have been produced by the I.F. beam formingnetwork they are fed to a bank of upconvertors 3730 for frequencytranslation to the desired satellite-mobile frequency band. Theupconvertors are all driven by the same local oscillator signal so as topreserve the relative phase of the signals, and have matched gain topreserve relative amplitudes. The upconverted signals may then beamplified by a matrix power amplifier 3740 to raise the power level tothe desired transmit power.

The inventive technique described above can be extended to produce anynumber of virtual beams associated with subdivisions of the totalfrequency band available. In the three-color example, each "color" isassociated with a 1/3rd sub-bandwidth. If 16.5 MHz total is available,for example, each transponder channel bandwidth can be nominally 5.5MHz. If the number of feeds is 37, for example, 37, 5.5 MHz "black"beams are generated, 37, 5.5 MHz wide red beams and 37, 5.5 MHz greenbeams. Thus the total bandwidth available for communication is 37 times16.5 MHz, as it would have been had it been possible to employ immediatefrequency re-use of all 16.5 MHz in the "black" beams only. Thus thepresent invention provides the same efficient use of bandwidth as animmediate frequency re-use pattern but with a considerably improved C/I.

The extra capacity thus available is, in the FDMA version, obtained byincreasing the number of transponder channels and thus hardwarecomplexity proportionally. It will now be shown how an exemplary TDMAembodiment can be advantageously constructed in which the capacityincrease is obtained without increased hardware complexity.

FIG. 39 illustrates the exemplary TDMA embodiment. In this case thenumber of transponder channels 3910 is the same as the number of antennafeeds, and the bandwidth of each channel is the full bandwidth availableto the system. The I.F. beam forming network 3920 also functions aspreviously described to synthesize black, red and green beams, but onlyone color is connected at a time to the set of transponder channels byvirtue of the commutating switches 3911. Either (1) all transponderchannels are connected to a corresponding number of "black" beam inputs,or, (2) by operating switches 3911 all at the same time, alltransponders are connected to the red beam inputs, or (3), as shown inFIG. 39, to the green beam inputs.

The switches are cycled such that for a first portion of a TDMA frameperiod (e.g., 1/3rd) the black beams are used, for a second portion ofthe time the red beams are energized, and for a third portion of thetime the green beams are energized. The time periods during which theswitches dwell in each position do not have to be equal, and can inprinciple be adapted according to which color has the highestinstantaneous capacity demand in any cell. The functioning of the restof the transponder is as previously described for the FDMA case.

It will be appreciated that the commutation of switches 3911 issynchronized with transmissions from the central ground station orstations, and this can be achieved by any of a variety of techniques,such as providing an on-board clock that can be programmed form theground to execute the regular cycle of switch operations and tosynchronize the ground station transmissions to the satellite, which isthe master timer. Alternatively a ground station can transmit a switchcommand using a control channel separate from the traffic channels. Themethod of achieving synchronism of the beam gyrations with the groundnetwork is immaterial to the principle of the present invention.

It may be appreciated that, although both the TDMA and FDMA versions ofthe invention disclosed above used fixed beam forming networks, it ispossible by an obvious extension of the method to permute the allocationof frequencies or time slots to beam colors by use of switches 3911controlled from the ground in such a way as to keep the areas of theearth illuminated by a given frequency or time slot as nearly aspossible fixed. This is of course achieved more accurately by usinggreater numbers of "colors" (that is timeslots or sub-bands). Increasingthe number of sub-bands involves hardware complexity in the FDMA case,so the TDMA version is preferred in this respect. The phasing of thecommutation switches may thus be chosen so as to compensate forsatellite motion and keep the areas illuminated by a particular timeslotor frequency more or less constant. The present invention can be appliedto any number of timeslots and sub-bands, and in the latter case adigital implementation comprising analog-to-digital conversion of thetransponder signals, digital filtering and digital beam forming usingdigital weight multiplication may be advantageous.

The above-described exemplary embodiments are intended to beillustrative in all respects, rather than restrictive, of the presentinvention. Thus the present invention is capable of many variations indetailed implementation that can be derived from the descriptioncontained herein by a person skilled in the art. All such variations andmodifications are considered to be within the scope and spirit of thepresent invention as defined by the following claims.

What is claimed is:
 1. A satellite communications system employing amultiple element antenna receiving signals on a first frequency band andrelaying said signals to a ground station on a second frequency bandincluding:downconverting means for converting signals received at eachof said multiple antenna elements on said first frequency band tocorresponding baseband signals; multiplexing means for directlyreceiving and time-division multiplexing said corresponding basebandsignals to form a multiplexed sample stream; and modulator means formodulating a carrier in said second frequency band with said multiplexedsample stream and transmitting said modulated carrier to said groundstation; wherein said downconverting means comprise quadraturedownconverting means producing an I and a Q baseband signals.
 2. Thesystem as in claim 1, in which said multiplexing means comprises anI-signal multiplexing means and a Q-signal multiplexing means.
 3. Thesystem as in claim 1, in which said modulator means comprises aquadrature modulator means in which an I signal and a Q signal areimpressed on respective carrier signals of nominally 90 degrees phasedifference.
 4. The system of claim 1, in which said multiplexing meanscomprises analog to digital conversion of said I and Q baseband signalsand digital multiplexing of the resultant digital streams to form I andQ bitstreams.
 5. The system of claim 4, in which said modulator meanscomprises a digital modulator means in which said multiplexed I and Qbit streams digitally modulate respective quadrature carriers at saidsecond frequency.
 6. The system of claims 1, in which said correspondingbaseband signals are representative of the instantaneous phase andamplitude respectively of said antenna signals relative to common phaseand amplitude references.
 7. A satellite communications system forrelaying signals received from a ground station on a second frequencyband by transmitting said signals on a first frequency band using amultiplicity of antenna elements, including:downconverting means forconverting signals received at said second frequency to a correspondingbaseband signal; demultiplexing means for time-division demultiplexingsaid corresponding baseband signal to obtain separate sample streams;separate modulator means corresponding to each of said separate samplestreams for directly receiving said separate sample streams and formodulating a carrier at said first frequency band with said separatesample streams to generate corresponding modulated signals; transmitamplifier means for amplifying said modulated signals and transmittingsaid modulated signals using said multiple antenna elements; whereinsaid downconverting means comprises a quadrature downconverting meansproducing an I and a Q baseband signal.
 8. The system as in claim 7, inwhich said demultiplexing means comprises an I-signal demultiplexingmeans and a Q-signal demultiplexing means and said separate samplestreams comprise I and Q sample streams.
 9. The system as in claim 8, inwhich said separate modulator means includes a quadrature modulatormeans in which an I sample stream and a Q sample stream are impressed onrespective carrier signals having nominally 90 degrees phase difference.10. The system of claim 7, in which said demultiplexing means is adigital demultiplexing means producing separate I and Q bitstreams. 11.The system of claim 10, in which said separate I and Q bitstreams areanalog to digital converted and filtered to form corresponding I and Qanalog waveforms.
 12. The system of claim 11, in which said I and Qwaveforms each modulate a carrier at said first frequency usingrespective quadrature modulators to generate said correspondingmodulated signals.
 13. The system of claim 7, in which saidcorresponding baseband signal includes an amplitude-corresponding signaland a phase-corresponding signal.
 14. The system of claim 17, in whichsaid separate modulator means comprise an amplitude modulator and aphase modulator.
 15. A bidirectional satellite communications systemcomprising:a satellite including: a multiple element antenna havingmultiple antenna elements for receiving signals on a first frequencyband and relaying said signals to a ground station on a second frequencyband; downconverting means for converting signals received at each ofsaid multiple antenna elements on said first frequency band tocorresponding baseband signals; multiplexing means for directlyreceiving and time-division multiplexing said corresponding basebandsignals to form a multiplexed sample stream; and modulator means formodulating a carrier in said second frequency band with said multiplexedsample stream and transmitting said modulated carrier to said groundstation and a ground station including: downconverting means forconverting signals received at said second frequency to a correspondingbaseband signal; demultiplexing means, for time-division demultiplexingsaid corresponding baseband signal to obtain separate sample streams;modulator means for modulating a carrier with signals to generatecorresponding modulated signals; transmit amplifier means for amplifyingsaid modulated signals and transmitting said signals to said satellite;and wherein said multiplexing means and said demultiplexing means aresynchronized.
 16. The system of claim 15, in which said ground stationfurther comprises:means for synchronizing said demultiplexing means to atime multiplexed signal received from said satellite on said secondfrequency band and synchronizing a second multiplexing means fortransmission of a time multiplexed signal to said satellite based onpropagation delay so that said transmitted signal will arrive insynchronism with a second demultiplexing means on board said satellite.17. The system of claim 16, in which said ground station synchronizessaid ground station demultiplexing means using pilot samples transmittedby said satellite in the multiplexed sample stream.
 18. The systemaccording to claim 17, in which said pilot symbols include the nullsymbol (0,0).
 19. The system according to claim 17, in which said pilotsymbols are used at said ground station to assist in synchronizing saidground station demultiplexer.
 20. The system according to claim 17, inwhich said pilot symbols are used at said ground station to correct fortransmission or modulation errors.
 21. The system according to claim 15,in which said ground station includes an equalizer for reducingintersample interference arising in the transmission of said multiplexedsample stream.
 22. The system of claim 15, in which said ground stationincludes a pre-equalizer to reduce intersample interference arising inthe transmission of said signals from said ground station to saidsatellite in said second frequency band.
 23. A satellite communicationssystem employing a multiple element antenna receiving signals on a firstfrequency band and relaying said signals to a ground station on a secondfrequency band including:downconverting means for converting signalsreceived at each of said multiple antenna elements on said firstfrequency band to corresponding baseband signals; multiplexing means fordirectly receiving and time-division multiplexing said correspondingbaseband signals to form a multiplexed sample stream; and modulatormeans for modulating a carrier in said second frequency band with saidmultiplexed sample stream and transmitting said modulated carrier tosaid ground station; wherein said multiplexing means comprises anI-signal multiplexing means and a Q-signal multiplexing means.
 24. Asatellite communications system employing a multiple element antennareceiving signals on a first frequency band and relaying said signals toa ground station on a second frequency band including:downconvertingmeans for converting signals received at each of said multiple antennaelements on said first frequency band to corresponding baseband signals;multiplexing means for directly receiving and time-division multiplexingsaid corresponding baseband signals to form a multiplexed sample stream;and modulator means for modulating a carrier in said second frequencyband with said multiplexed sample stream and transmitting said modulatedcarrier to said ground station; wherein said modulator means comprises aquadrature modulator means in which an I signal and a Q signal areimpressed on respective carrier signals of nominally 90 degrees phasedifference.
 25. A satellite communications system for relaying signalsreceived from a ground station on a second frequency band bytransmitting said signals on a first frequency band using a multiplicityof antenna elements, including:downconverting means for convertingsignals received at said second frequency to a corresponding basebandsignal; demultiplexing means for time-division demultiplexing saidcorresponding baseband signal to obtain separate sample streams;separate modulator means corresponding to each of said separate samplestreams for directly receiving said separate sample streams and formodulating a carrier at said first frequency band with said separatesample streams to generate corresponding modulated signals; transmitamplifier means for amplifying said modulated signals and transmittingsaid modulated signals using said multiple antenna elements; whereinsaid demultiplexing means comprises an I-signal demultiplexing means anda Q-signal demultiplexing means and said separate sample streamscomprise I and Q sample streams.
 26. A communications system employing asatellite having a multiple element antenna having multiple antennaelements for receiving signals on a first frequency band and relayingsaid signals to a ground station on a second frequency bandincluding:satellite downconverting means for converting signals receivedat each of said multiple antenna elements on said first frequency bandto corresponding baseband signals; satellite multiplexing means fordirectly receiving and time-division multiplexing said correspondingbaseband signals to form a multiplexed sample stream; satellitemodulator means for modulating a carrier in said second frequency bandwith said multiplexed sample stream and transmitting said modulatedcarrier to said ground station; ground station receiving means forreceiving said multiplexed sample stream from said satellite modulatormeans; ground station demultiplexing means for time-divisiondemultiplexing said multiplexed sample stream to form separate samplestreams; and ground station routing means for routing said separatesample streams to appropriate destination terminals.
 27. Thecommunication system of claim 26, wherein said satellite multiplexingmeans further comprises means for multiplexing a reference signal fortransmission to said ground station, for use by said ground stationdemultiplexing means in synchronizing its operation to said satellitemultiplexing means.
 28. The communications system of claim 27, whereinsaid reference signal comprises a complex analog reference sample. 29.The communication system of claim 26, wherein said satellitemultiplexing means forms a singular multiplexed sample stream whichcombines all of the signals received by said multiple antenna elements.30. The communication system of claim 26, wherein said baseband signalsare fed from said satellite downconverting means directly to saidsatellite multiplexing means.
 31. The communication system of claim 26,wherein said satellite multiplexing means comprises plural multiplexersfor forming plural multiplexed sample streams, wherein each multiplexedsample stream corresponds to a separate frequency-division-multiplexedcarrier received by said multiple antenna elements.
 32. A satellitecommunications system employing a multiple element antenna receivingsignals on a first frequency band and relaying said signals to a groundstation on a second frequency band including:downconverting means forconverting signals received at each of said multiple antenna elements onsaid first frequency band to corresponding baseband signals;multiplexing means for directly receiving and time-division multiplexingsaid corresponding baseband signals to form a multiplexed sample stream;modulator means for modulating a carrier in said second frequency bandwith said multiplexed sample stream and transmitting said modulatedcarrier to said ground station; and a time-division demultiplexing meansfor processing time-division multiplexed signals received from saidground station, wherein said demultiplexing means and said multiplexingmeans use a same clock.
 33. The communications system of claim 1,wherein said satellite multiplexing means forms a singular multiplexedsample stream which combines all of the signals received by saidmultiple antenna elements.
 34. The communications system of claim 7,wherein said satellite demultiplexing means receives a singularmultiplexed sample stream.
 35. The communications system of claim 15,wherein said satellite multiplexing means forms a singular multiplexedsample stream which combines all of the signals received by saidmultiple antenna elements.
 36. The communications system of claim 23,wherein said satellite multiplexing means forms a singular multiplexedsample stream which combines all of the signals received by saidmultiple antenna elements.
 37. The communications system of claim 24,wherein said satellite multiplexing means forms a singular multiplexedsample stream which combines all of the signals received by saidmultiple antenna elements.
 38. The communications system of claim 25,wherein said satellite demultiplexing means receives a singularmultiplexed sample stream.
 39. The communications system of claim 32,wherein said satellite multiplexing means forms a singular multiplexedsample stream which combines all of the signals received by saidmultiple antenna elements.